Algebra 334

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 4, 5, 6, 2 ] 
[ 4, 5, 6, 2, 8, 3 ] 
[ 5, 6, 2, 8, 3, 4 ] 
[ 6, 2, 8, 3, 4, 5 ] 
[ 6, 2, 7 ] 
[ 3, 4, 5, 6, 2, 8 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 4, 5, 6 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(0 1 1 1 1 1 1 1)
(0 1 1 1 1 1 0 0)
(0 1 0 1 1 1 0 1)
(0 1 1 0 1 1 0 1)
(0 1 1 1 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  493    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  796    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  337    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  798    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 337

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 7, 5, 2 ] 
[ 8, 3, 4, 5, 2 ] 
[ 4, 5, 2, 8, 3 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 5, 2, 7 ] 
[ 3, 4, 5, 2, 8 ] 
[ 5, 2, 8, 3, 4 ] - [ 5, 6, 4 ] 
[ 2, 7, 5 ] - [ 2, 8, 3, 4, 5 ] 

Cartan matrix

(1 1 1 1 1 0 1 1)
(0 1 1 1 1 0 1 1)
(0 1 1 1 1 0 0 0)
(0 1 0 1 1 0 0 1)
(0 1 1 1 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  496    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  803    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  374    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  334    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  648    permutation [ 5, 1, 2, 8, 3, 4, 6, 7 ]
vertex  8 -> Algebra  804    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 347

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 4, 2 ] 
[ 8, 2, 3 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 4, 2, 3 ] - [ 4, 5, 3 ] 
[ 2, 3, 4 ] - [ 2, 6, 4 ] 

Cartan matrix

(1 1 1 1 0 1 1 0)
(0 1 1 1 0 1 1 0)
(0 1 1 1 0 0 0 1)
(0 1 1 1 1 0 0 0)
(0 0 1 0 1 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  506    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  825    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  822    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  824    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 374

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 7, 5, 2 ] 
[ 8, 3, 5, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 3, 5 ] 
[ 3, 5, 6 ] 
[ 5, 2, 7 ] 
[ 5, 2, 8, 3 ] - [ 5, 6, 3 ] 
[ 2, 7, 5 ] - [ 2, 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 2, 8 ] 

Cartan matrix

(1 1 1 0 1 0 1 1)
(0 1 1 0 1 0 1 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 1)
(0 1 1 0 1 1 0 1)
(0 0 1 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  531    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  337    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  650    permutation [ 5, 1, 2, 8, 3, 4, 6, 7 ]
vertex  8 -> Algebra  878    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 493

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 4, 5, 6, 2 ] 
[ 4, 5, 6, 2, 8, 3 ] 
[ 5, 6, 2, 8, 3, 4 ] 
[ 6, 2, 8, 3, 4, 5 ] 
[ 6, 2, 7 ] 
[ 3, 4, 5, 6, 2, 8 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 4, 5, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 1 1)
(1 1 1 1 1 1 0 0)
(1 1 0 1 1 1 0 1)
(1 1 1 0 1 1 0 1)
(1 1 1 1 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  334    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  996    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  496    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  998    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 496

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 7, 5, 2 ] 
[ 8, 3, 4, 5, 2 ] 
[ 4, 5, 2, 8, 3 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 5, 2, 7 ] 
[ 3, 4, 5, 2, 8 ] 
[ 5, 2, 8, 3, 4 ] - [ 5, 6, 4 ] 
[ 2, 7, 5 ] - [ 2, 8, 3, 4, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 1 1)
(1 1 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  337    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1002    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  531    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  493    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  754    permutation [ 5, 2, 1, 8, 3, 4, 6, 7 ]
vertex  8 -> Algebra 1003    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 506

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 4, 2 ] 
[ 8, 2, 3 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 4, 2, 3 ] - [ 4, 5, 3 ] 
[ 2, 3, 4 ] - [ 2, 6, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 1 1 0)
(1 1 1 1 0 0 0 1)
(1 1 1 1 1 0 0 0)
(0 0 1 0 1 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  347    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1020    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1017    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1019    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 531

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 7, 5, 2 ] 
[ 8, 3, 5, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 3, 5 ] 
[ 3, 5, 6 ] 
[ 5, 2, 7 ] 
[ 5, 2, 8, 3 ] - [ 5, 6, 3 ] 
[ 2, 7, 5 ] - [ 2, 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 0 1 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 1)
(1 1 1 0 1 1 0 1)
(0 0 1 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  374    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1054    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  496    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  756    permutation [ 5, 2, 1, 8, 3, 4, 6, 7 ]
vertex  8 -> Algebra 1055    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 648

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 1 ] 
[ 8, 3, 4, 5, 6, 1 ] 
[ 4, 5, 6, 1, 8, 3 ] 
[ 5, 6, 1, 8, 3, 4 ] 
[ 6, 1, 8, 3, 4, 5 ] 
[ 6, 1, 7 ] 
[ 3, 4, 5, 6, 1, 8 ] 
[ 1, 7, 6 ] - [ 1, 8, 3, 4, 5, 6 ] 

Cartan matrix

(1 0 1 1 1 1 1 1)
(1 1 1 1 1 1 0 0)
(1 0 1 1 1 1 0 0)
(1 0 0 1 1 1 0 1)
(1 0 1 0 1 1 0 1)
(1 0 1 1 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra  754    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  678    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  650    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  337    permutation [ 2, 3, 5, 6, 1, 7, 8, 4 ]

Algebra 650

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 7, 5, 1 ] 
[ 8, 3, 4, 5, 1 ] 
[ 4, 5, 1, 8, 3 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 5, 1, 7 ] 
[ 3, 4, 5, 1, 8 ] 
[ 5, 1, 8, 3, 4 ] - [ 5, 6, 4 ] 
[ 1, 7, 5 ] - [ 1, 8, 3, 4, 5 ] 

Cartan matrix

(1 0 1 1 1 0 1 1)
(1 1 1 1 1 0 0 0)
(1 0 1 1 1 0 0 0)
(1 0 0 1 1 0 0 1)
(1 0 1 1 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  756    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  648    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  871    permutation [ 2, 3, 5, 6, 7, 1, 8, 4 ]
vertex  8 -> Algebra  374    permutation [ 2, 3, 5, 6, 1, 7, 8, 4 ]

Algebra 657

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 6, 4, 1 ] 
[ 8, 1, 3 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 1, 6 ] 
[ 1, 3, 8 ] 
[ 3, 4, 1 ] - [ 3, 8, 1 ] 
[ 4, 1, 3 ] - [ 4, 5, 3 ] 
[ 1, 3, 4 ] - [ 1, 6, 4 ] 

Cartan matrix

(1 0 1 1 0 1 1 0)
(1 1 1 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 0 1 1 1 0 0 0)
(0 0 1 0 1 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra  763    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1168    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  804    permutation [ 2, 3, 4, 6, 1, 7, 8, 5 ]
vertex  7 -> Algebra  828    permutation [ 2, 3, 4, 1, 7, 6, 8, 5 ]

Algebra 678

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 8 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 1 ] 
[ 8, 3, 5, 6, 1 ] 
[ 3, 4, 2 ] 
[ 5, 6, 1, 8, 3 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 6, 1, 8, 3, 5 ] 
[ 6, 1, 7 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 1, 7, 6 ] - [ 1, 8, 3, 5, 6 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 1, 8 ] 

Cartan matrix

(1 0 1 0 1 1 1 1)
(1 1 1 0 1 1 0 0)
(1 0 1 1 1 1 0 1)
(0 1 1 1 1 1 0 1)
(1 0 0 0 1 1 0 1)
(1 0 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 0 1 1 0 1)

Good mutations

vertex  2 -> Algebra  857    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  648    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1186    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 724

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 6, 4, 1 ] 
[ 3, 4, 8, 2 ] 
[ 1, 6, 4 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 3, 4, 8 ] 
[ 6, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] - [ 8, 6, 4 ] 
[ 4, 1, 6 ] - [ 4, 8, 6 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 1 1 1)
(1 1 1 1 1 1 1 1)
(0 0 1 0 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1239    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  936    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  738    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  784    permutation [ 4, 8, 1, 7, 2, 3, 5, 6 ]
vertex  7 -> Algebra 1002    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1168    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 738

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 6, 5, 1 ] 
[ 3, 4, 5, 8, 2 ] 
[ 4, 5, 8, 2, 3 ] 
[ 5, 8, 2, 3, 4 ] 
[ 1, 6, 5 ] 
[ 2, 3, 4, 5, 8 ] 
[ 6, 5, 8 ] 
[ 8, 2, 3, 4, 5 ] - [ 8, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 1 1 1 0 0 0)
(1 0 1 1 1 1 1 1)
(1 1 0 1 1 1 1 1)
(1 1 1 0 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1246    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  724    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  996    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1248    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 754

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 7, 6, 1 ] 
[ 8, 2, 4, 5, 6, 1 ] 
[ 4, 5, 6, 1, 8, 2 ] 
[ 5, 6, 1, 8, 2, 4 ] 
[ 6, 1, 8, 2, 4, 5 ] 
[ 6, 1, 7 ] 
[ 2, 4, 5, 6, 1, 8 ] 
[ 1, 7, 6 ] - [ 1, 8, 2, 4, 5, 6 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 1 1 1 0 0)
(0 0 1 0 0 0 0 0)
(1 0 0 1 1 1 0 1)
(1 1 1 0 1 1 0 1)
(1 1 1 1 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra  784    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  648    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  756    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  496    permutation [ 3, 2, 5, 6, 1, 7, 8, 4 ]

Algebra 756

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 7, 5, 1 ] 
[ 8, 2, 4, 5, 1 ] 
[ 4, 5, 1, 8, 2 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 5, 1, 7 ] 
[ 2, 4, 5, 1, 8 ] 
[ 5, 1, 8, 2, 4 ] - [ 5, 6, 4 ] 
[ 1, 7, 5 ] - [ 1, 8, 2, 4, 5 ] 

Cartan matrix

(1 1 1 1 1 0 1 1)
(1 1 1 1 1 0 0 0)
(0 0 1 0 0 0 0 0)
(1 0 0 1 1 0 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  786    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  650    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  754    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1048    permutation [ 3, 2, 5, 6, 7, 1, 8, 4 ]
vertex  8 -> Algebra  531    permutation [ 3, 2, 5, 6, 1, 7, 8, 4 ]

Algebra 763

Quiver

[ 1, 2 ], [ 1, 6 ], [ 2, 3 ], [ 2, 4 ], [ 2, 8 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 4 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 6, 4, 1 ] 
[ 8, 1, 2 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 4, 1, 6 ] 
[ 1, 2, 8 ] 
[ 2, 4, 1 ] - [ 2, 8, 1 ] 
[ 4, 1, 2 ] - [ 4, 5, 2 ] 
[ 1, 2, 4 ] - [ 1, 6, 4 ] 

Cartan matrix

(1 1 1 1 0 1 1 0)
(1 1 1 1 0 0 0 1)
(0 0 1 0 0 0 0 0)
(1 1 1 1 1 0 0 0)
(0 1 1 0 1 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1258    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  657    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1003    permutation [ 3, 2, 4, 6, 1, 7, 8, 5 ]
vertex  7 -> Algebra 1023    permutation [ 3, 2, 4, 1, 7, 6, 8, 5 ]

Algebra 784

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 6, 1 ] 
[ 8, 2, 5, 6, 1 ] 
[ 4, 8, 2 ] 
[ 5, 6, 1, 8, 2 ] 
[ 4, 8, 3 ] 
[ 6, 1, 8, 2, 5 ] 
[ 6, 1, 7 ] 
[ 3, 4, 8 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 1, 7, 6 ] - [ 1, 8, 2, 5, 6 ] 
[ 2, 4, 8 ] - [ 2, 5, 6, 1, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 0 1 1 1 0 1)
(0 0 1 1 0 0 0 0)
(0 0 0 1 0 0 0 1)
(1 0 1 0 1 1 0 1)
(1 1 1 1 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1236    permutation [ 3, 5, 6, 8, 7, 1, 4, 2 ]
vertex  2 -> Algebra  793    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  857    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  754    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra  786    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  724    permutation [ 3, 5, 6, 1, 7, 8, 4, 2 ]

Algebra 786

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 2 ], [ 7, 5 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 5, 1 ] 
[ 8, 2, 5, 1 ] 
[ 4, 8, 2 ] 
[ 4, 8, 3 ] 
[ 6, 2, 5 ] 
[ 2, 5, 6 ] 
[ 5, 1, 7 ] 
[ 3, 4, 8 ] 
[ 5, 1, 8, 2 ] - [ 5, 6, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 1, 7, 5 ] - [ 1, 8, 2, 5 ] 
[ 2, 4, 8 ] - [ 2, 5, 1, 8 ] 

Cartan matrix

(1 1 1 1 1 0 1 1)
(1 1 0 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(0 0 0 1 0 0 0 1)
(1 1 1 1 1 1 0 1)
(0 1 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1272    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  803    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra  756    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra  784    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1273    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  936    permutation [ 3, 5, 6, 1, 7, 8, 4, 2 ]

Algebra 793

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 6, 1 ] 
[ 8, 2, 6, 1 ] 
[ 5, 8, 2 ] 
[ 6, 1, 8, 2 ] 
[ 4, 5, 8, 3 ] 
[ 5, 8, 3, 4 ] 
[ 6, 1, 7 ] 
[ 3, 4, 5, 8 ] 
[ 8, 2, 5 ] - [ 8, 3, 4, 5 ] 
[ 1, 7, 6 ] - [ 1, 8, 2, 6 ] 
[ 2, 5, 8 ] - [ 2, 6, 1, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 0 1 1 0 1)
(0 0 1 1 1 0 0 0)
(0 0 0 1 1 0 0 1)
(0 0 1 0 1 0 0 1)
(1 0 1 1 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1278    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  796    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra  867    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  784    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  8 -> Algebra 1280    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 796

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 6, 8, 2 ] 
[ 4, 5, 6, 8, 3 ] 
[ 5, 6, 8, 3, 4 ] 
[ 6, 8, 3, 4, 5 ] 
[ 2, 1, 7 ] 
[ 3, 4, 5, 6, 8 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 3, 4, 5, 6 ] 
[ 2, 1, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 1 0 1 0 1)
(0 0 1 1 1 1 0 0)
(0 0 0 1 1 1 0 1)
(0 0 1 0 1 1 0 1)
(0 0 1 1 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1283    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  334    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  870    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  803    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  793    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  8 -> Algebra 1285    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 798

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 7, 6, 2 ] 
[ 4, 5, 6, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 6, 2, 3, 4 ] 
[ 6, 2, 3, 4, 5 ] 
[ 6, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 6, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4, 5, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(0 1 1 1 1 1 1 0)
(0 1 1 1 1 1 0 1)
(0 1 0 1 1 1 0 0)
(0 1 1 0 1 1 0 0)
(0 1 1 1 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra  998    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1286    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  822    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  804    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1166    permutation [ 6, 1, 2, 3, 8, 4, 5, 7 ]
vertex  8 -> Algebra  334    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 799

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 5, 6, 2 ] 
[ 4, 5, 6, 2, 8, 3 ] 
[ 5, 6, 2, 8, 3, 4 ] 
[ 2, 8, 3, 4, 5, 6 ] 
[ 7, 5, 6 ] 
[ 5, 6, 7 ] 
[ 3, 4, 5, 6, 2, 8 ] 
[ 6, 2, 8, 3, 4, 5 ] - [ 6, 7, 5 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(0 1 1 1 1 1 0 0)
(0 1 0 1 1 1 0 1)
(0 1 1 0 1 1 0 1)
(0 1 1 1 1 1 1 1)
(0 0 0 0 1 0 1 0)
(0 0 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  999    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1288    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  823    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]

Algebra 803

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 5, 8, 2 ] 
[ 4, 5, 8, 3 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 2, 1, 7 ] 
[ 3, 4, 5, 8 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 5, 6, 4 ] - [ 5, 8, 3, 4 ] 
[ 8, 2, 5 ] - [ 8, 3, 4, 5 ] 
[ 2, 1, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 1 1 1 1 0 1 1)
(1 1 1 1 1 1 0 1)
(0 0 1 1 1 0 0 0)
(0 0 0 1 1 0 0 1)
(0 0 1 1 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 1 0 0 1 1 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1295    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  337    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  786    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra  796    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1186    permutation [ 5, 1, 8, 7, 3, 4, 6, 2 ]
vertex  8 -> Algebra 1296    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 804

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 7, 5, 2 ] 
[ 4, 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 5, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 2 ] - [ 3, 8, 2 ] 
[ 5, 2, 3, 4 ] - [ 5, 6, 4 ] 
[ 2, 3, 4, 5 ] - [ 2, 7, 5 ] 

Cartan matrix

(1 1 1 1 1 0 1 0)
(0 1 1 1 1 0 1 0)
(0 1 1 1 1 0 0 1)
(0 1 0 1 1 0 0 0)
(0 1 1 1 1 1 0 0)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1003    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1280    permutation [ 2, 1, 5, 6, 4, 7, 8, 3 ]
vertex  3 -> Algebra 1171    permutation [ 5, 1, 2, 4, 8, 3, 6, 7 ]
vertex  4 -> Algebra  657    permutation [ 5, 1, 2, 3, 8, 4, 6, 7 ]
vertex  6 -> Algebra  798    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  337    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 819

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 8 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 3, 8, 1 ] 
[ 6, 2, 8, 1 ] 
[ 8, 1, 6, 2 ] 
[ 5, 3, 8, 4 ] 
[ 3, 8, 4, 5 ] 
[ 2, 8, 1, 6 ] 
[ 4, 5, 3, 8 ] 
[ 8, 1, 3 ] - [ 8, 4, 5, 3 ] 
[ 1, 3, 8 ] - [ 1, 6, 2, 8 ] 

Cartan matrix

(1 1 1 1 0 1 1 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 1 0 1 0 0 1)
(0 1 0 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1224    permutation [ 3, 2, 8, 6, 7, 4, 5, 1 ]
vertex  2 -> Algebra  825    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1306    permutation [ 3, 6, 1, 7, 2, 8, 5, 4 ]
vertex  4 -> Algebra 1258    permutation [ 1, 8, 3, 2, 5, 6, 7, 4 ]
vertex  6 -> Algebra 1286    permutation [ 2, 1, 8, 4, 5, 3, 6, 7 ]
vertex  7 -> Algebra 1313    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 821

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 7 ], [ 7, 2 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 6, 7, 2 ] 
[ 5, 3, 4 ] 
[ 6, 7, 2, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 7, 2, 8, 3, 4, 6 ] 
[ 2, 8, 3, 4, 6, 7 ] 
[ 3, 4, 6, 7, 2, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 7, 2, 8, 3 ] 

Cartan matrix

(1 1 1 1 0 1 0 1)
(0 1 1 1 0 1 0 1)
(0 1 1 1 0 1 1 0)
(0 1 1 1 1 1 1 1)
(0 0 1 0 1 0 0 0)
(0 1 1 0 0 1 1 1)
(0 1 1 1 0 0 1 1)
(0 0 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1016    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1187    permutation [ 6, 1, 8, 2, 3, 4, 5, 7 ]
vertex  6 -> Algebra  823    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1167    permutation [ 6, 1, 2, 3, 8, 4, 5, 7 ]

Algebra 822

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 7, 6, 2 ] 
[ 8, 2, 3 ] 
[ 5, 3, 4 ] 
[ 6, 2, 3, 4 ] 
[ 3, 4, 5 ] 
[ 6, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 6, 2 ] - [ 3, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 6, 2, 3 ] 
[ 2, 3, 4, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 1 1 1 0 1 1 0)
(0 1 1 1 0 1 1 0)
(0 1 1 1 0 1 0 1)
(0 1 1 1 1 1 0 0)
(0 0 1 0 1 0 0 1)
(0 1 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1017    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1317    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  828    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra  798    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  347    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1167    permutation [ 6, 1, 2, 3, 8, 4, 5, 7 ]

Algebra 823

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 7, 4 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 6, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 8, 3, 4, 6 ] 
[ 7, 4, 6 ] 
[ 4, 6, 7 ] 
[ 3, 4, 6, 2, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 2, 8, 3 ] 
[ 6, 2, 8, 3, 4 ] - [ 6, 7, 4 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 1 1 1 0 1 0 0)
(0 1 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(0 1 1 1 0 1 1 1)
(0 0 0 1 1 0 1 0)
(0 0 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1018    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1318    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  799    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  821    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1319    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 824

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 6, 4, 2 ] 
[ 8, 2, 3 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 4, 2, 3 ] - [ 4, 5, 3 ] 
[ 2, 3, 4 ] - [ 2, 6, 4 ] 

Cartan matrix

(1 1 1 1 0 1 0 0)
(0 1 1 1 0 1 0 0)
(0 1 1 1 0 0 0 1)
(0 1 1 1 1 0 0 0)
(0 0 1 0 1 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 1 1 1 1 0)
(0 1 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1019    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1320    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1319    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  347    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 825

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 3, 2, 1 ] 
[ 6, 2, 1 ] 
[ 4, 5, 3, 2 ] 
[ 8, 6, 2 ] 
[ 5, 3, 2, 4 ] 
[ 3, 2, 4, 5 ] 
[ 6, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 6, 2 ] 
[ 2, 1, 3 ] - [ 2, 4, 5, 3 ] 
[ 2, 1, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 1 1 0 1 1 0)
(1 1 1 1 1 1 1 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 1 1 0 1 0 0 1)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1322    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  347    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1300    permutation [ 3, 6, 1, 7, 2, 8, 5, 4 ]
vertex  4 -> Algebra  836    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1323    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1320    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  819    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 828

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 7, 4, 2 ] 
[ 8, 2, 3 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 4, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 4, 2, 3 ] - [ 4, 6, 3 ] 
[ 2, 3, 4 ] - [ 2, 7, 4 ] 

Cartan matrix

(1 1 1 1 0 0 1 0)
(0 1 1 1 0 0 1 0)
(0 1 1 1 0 0 0 1)
(0 1 1 1 0 1 0 0)
(0 0 1 0 1 1 0 1)
(0 0 1 0 0 1 0 1)
(0 0 0 1 0 1 1 0)
(0 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1023    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1326    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  657    permutation [ 4, 1, 2, 3, 8, 6, 5, 7 ]
vertex  6 -> Algebra  822    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]

Algebra 836

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 3, 4, 1 ] 
[ 6, 4, 1 ] 
[ 4, 5, 2 ] 
[ 8, 6, 4 ] 
[ 2, 4, 5 ] 
[ 3, 4, 5 ] 
[ 6, 4, 8 ] 
[ 4, 1, 3 ] - [ 4, 5, 3 ] 
[ 1, 3, 4 ] - [ 1, 6, 4 ] 
[ 5, 2, 4 ] - [ 5, 3, 4 ] 
[ 4, 1, 6 ] - [ 4, 8, 6 ] 

Cartan matrix

(1 0 1 1 0 1 1 0)
(1 1 0 1 0 1 1 1)
(0 0 1 1 0 0 0 1)
(1 0 1 1 1 1 1 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1333    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  825    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1334    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1335    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1331    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1258    permutation [ 1, 4, 3, 8, 5, 6, 7, 2 ]

Algebra 857

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 7, 6, 1 ] 
[ 8, 2, 5, 6, 1 ] 
[ 3, 4, 8, 2 ] 
[ 5, 6, 1, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 6, 1, 8, 2, 5 ] 
[ 6, 1, 7 ] 
[ 1, 7, 6 ] - [ 1, 8, 2, 5, 6 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 6, 1, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 1 1 1 1 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 1 1 0 1)
(1 0 0 0 1 1 0 1)
(1 1 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1363    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  867    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  678    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  784    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1365    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 867

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 6, 1 ] 
[ 8, 2, 6, 1 ] 
[ 5, 8, 2 ] 
[ 6, 1, 8, 2 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 1, 7 ] 
[ 8, 2, 5 ] - [ 8, 3, 5 ] 
[ 1, 7, 6 ] - [ 1, 8, 2, 6 ] 
[ 2, 5, 8 ] - [ 2, 6, 1, 8 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 0 0 1 1 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 0 1 0 1)
(0 0 0 0 1 0 0 1)
(1 0 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1383    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  870    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  4 -> Algebra  793    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  857    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  8 -> Algebra 1385    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 870

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 6 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 6, 8, 2 ] 
[ 4, 8, 3 ] 
[ 5, 6, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 8, 3, 5 ] 
[ 2, 1, 7 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 3, 5, 6 ] 
[ 2, 1, 8 ] - [ 2, 6, 8 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 1 0 0 1 0 1)
(0 0 1 1 1 1 0 1)
(0 1 0 1 0 0 0 1)
(0 0 0 0 1 1 0 1)
(0 0 1 0 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1390    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  796    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  867    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  8 -> Algebra 1392    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 871

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 6 ], [ 6, 7 ], [ 7, 2 ], [ 8, 3 ]

Relations

[ 8, 3, 5, 6, 7, 2 ] 
[ 4, 8, 3 ] 
[ 5, 6, 7, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 7, 2, 8, 3, 5 ] 
[ 7, 2, 8, 3, 5, 6 ] 
[ 2, 8, 3, 5, 6, 7 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 7, 2, 8 ] 

Cartan matrix

(1 1 1 0 1 1 0 1)
(0 1 1 0 1 1 0 1)
(0 1 1 1 1 1 1 1)
(0 0 0 1 0 0 0 1)
(0 1 0 0 1 1 1 1)
(0 1 1 0 0 1 1 1)
(0 1 1 0 1 0 1 1)
(0 0 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1048    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  650    permutation [ 6, 1, 2, 8, 3, 4, 5, 7 ]

Algebra 878

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 5 ], [ 3, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 7, 5, 2 ] 
[ 8, 2, 3 ] 
[ 6, 3, 5 ] 
[ 3, 5, 6 ] 
[ 5, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 5, 2 ] - [ 3, 8, 2 ] 
[ 5, 2, 3 ] - [ 5, 6, 3 ] 
[ 2, 3, 5 ] - [ 2, 7, 5 ] 

Cartan matrix

(1 1 1 0 1 0 1 0)
(0 1 1 0 1 0 1 0)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 1 0 1 1 0 0)
(0 0 1 1 0 1 0 1)
(0 0 0 0 1 1 1 0)
(0 1 0 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1055    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1245    permutation [ 1, 5, 6, 3, 7, 8, 4, 2 ]
vertex  4 -> Algebra 1171    permutation [ 5, 1, 2, 3, 4, 8, 6, 7 ]
vertex  8 -> Algebra  374    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 936

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 4 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 6, 4 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 6, 4, 1 ] 
[ 3, 8, 2 ] 
[ 8, 2, 3 ] 
[ 1, 6, 4 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 6, 4, 8 ] 
[ 4, 5, 2 ] - [ 4, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 6, 4 ] 
[ 4, 1, 6 ] - [ 4, 8, 6 ] 
[ 2, 3, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 1 1 0 1 1 1)
(0 0 1 0 0 1 1 1)
(1 1 0 1 1 1 1 1)
(0 1 1 0 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 0 1 1 1)

Good mutations

vertex  3 -> Algebra  724    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  786    permutation [ 4, 8, 1, 7, 2, 3, 5, 6 ]
vertex  7 -> Algebra 1054    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1334    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 996

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 1 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 6, 1 ] 
[ 4, 5, 6, 8, 3 ] 
[ 5, 6, 8, 3, 4 ] 
[ 6, 8, 3, 4, 5 ] 
[ 1, 2, 6 ] 
[ 2, 6, 8 ] 
[ 3, 4, 5, 6, 8 ] 
[ 6, 1, 2 ] - [ 6, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 3, 4, 5, 6 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 1 0 0)
(1 0 1 1 1 1 0 0)
(1 1 0 1 1 1 0 1)
(1 1 1 0 1 1 0 1)
(1 1 1 1 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1283    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  493    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1002    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  738    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1325    permutation [ 3, 5, 8, 1, 7, 2, 4, 6 ]

Algebra 998

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 7, 6, 2 ] 
[ 4, 5, 6, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 6, 2, 3, 4 ] 
[ 6, 2, 3, 4, 5 ] 
[ 6, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 6, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4, 5, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 1 0)
(1 1 1 1 1 1 0 1)
(1 1 0 1 1 1 0 0)
(1 1 1 0 1 1 0 0)
(1 1 1 1 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra  798    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1316    permutation [ 3, 5, 2, 8, 7, 1, 4, 6 ]
vertex  4 -> Algebra 1017    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1003    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1256    permutation [ 6, 2, 1, 3, 8, 4, 5, 7 ]
vertex  8 -> Algebra  493    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 999

Quiver

[ 2, 1 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 5, 6, 2 ] 
[ 4, 5, 6, 2, 8, 3 ] 
[ 5, 6, 2, 8, 3, 4 ] 
[ 2, 8, 3, 4, 5, 6 ] 
[ 7, 5, 6 ] 
[ 5, 6, 7 ] 
[ 3, 4, 5, 6, 2, 8 ] 
[ 6, 2, 8, 3, 4, 5 ] - [ 6, 7, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(1 1 1 1 1 1 0 0)
(1 1 0 1 1 1 0 1)
(1 1 1 0 1 1 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 0 1 0 1 0)
(0 0 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  799    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1018    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]

Algebra 1002

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 5, 1 ] 
[ 4, 5, 8, 3 ] 
[ 1, 2, 5 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 2, 5, 8 ] 
[ 3, 4, 5, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 2 ] 
[ 5, 6, 4 ] - [ 5, 8, 3, 4 ] 
[ 8, 2, 5 ] - [ 8, 3, 4, 5 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 1 0 0)
(1 0 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 1 0 0 1 1 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1295    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  496    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1054    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  996    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  724    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1326    permutation [ 3, 5, 8, 1, 7, 2, 4, 6 ]

Algebra 1003

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 7, 5, 2 ] 
[ 4, 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 5, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 2 ] - [ 3, 8, 2 ] 
[ 5, 2, 3, 4 ] - [ 5, 6, 4 ] 
[ 2, 3, 4, 5 ] - [ 2, 7, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 1 0)
(1 1 1 1 1 0 0 1)
(1 1 0 1 1 0 0 0)
(1 1 1 1 1 1 0 0)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra  804    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1317    permutation [ 3, 5, 2, 8, 7, 1, 4, 6 ]
vertex  3 -> Algebra 1261    permutation [ 5, 2, 1, 4, 8, 3, 6, 7 ]
vertex  4 -> Algebra  763    permutation [ 5, 2, 1, 3, 8, 4, 6, 7 ]
vertex  6 -> Algebra  998    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  496    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1016

Quiver

[ 2, 1 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 7 ], [ 7, 2 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 6, 7, 2 ] 
[ 5, 3, 4 ] 
[ 6, 7, 2, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 7, 2, 8, 3, 4, 6 ] 
[ 2, 8, 3, 4, 6, 7 ] 
[ 3, 4, 6, 7, 2, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 7, 2, 8, 3 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 1 0 1)
(1 1 1 1 0 1 1 0)
(1 1 1 1 1 1 1 1)
(0 0 1 0 1 0 0 0)
(1 1 1 0 0 1 1 1)
(1 1 1 1 0 0 1 1)
(0 0 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra  821    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1220    permutation [ 1, 3, 4, 5, 6, 7, 2, 8 ]
vertex  6 -> Algebra 1018    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1257    permutation [ 6, 2, 1, 3, 8, 4, 5, 7 ]

Algebra 1017

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 7, 6, 2 ] 
[ 8, 2, 3 ] 
[ 5, 3, 4 ] 
[ 6, 2, 3, 4 ] 
[ 3, 4, 5 ] 
[ 6, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 6, 2 ] - [ 3, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 6, 2, 3 ] 
[ 2, 3, 4, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 1 1 0)
(1 1 1 1 0 1 0 1)
(1 1 1 1 1 1 0 0)
(0 0 1 0 1 0 0 1)
(1 1 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra  822    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1463    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1023    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra  998    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  506    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1257    permutation [ 6, 2, 1, 3, 8, 4, 5, 7 ]

Algebra 1018

Quiver

[ 2, 1 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 7, 4 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 6, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 8, 3, 4, 6 ] 
[ 7, 4, 6 ] 
[ 4, 6, 7 ] 
[ 3, 4, 6, 2, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 2, 8, 3 ] 
[ 6, 2, 8, 3, 4 ] - [ 6, 7, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 0 0 1)
(1 1 1 1 0 1 0 0)
(1 1 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(1 1 1 1 0 1 1 1)
(0 0 0 1 1 0 1 0)
(0 0 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra  823    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  999    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra 1016    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1464    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1019

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 6, 4, 2 ] 
[ 8, 2, 3 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 4, 2, 3 ] - [ 4, 5, 3 ] 
[ 2, 3, 4 ] - [ 2, 6, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 1 0 0)
(1 1 1 1 0 0 0 1)
(1 1 1 1 1 0 0 0)
(0 0 1 0 1 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 1 1 1 1 0)
(1 1 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  824    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1418    permutation [ 3, 4, 8, 7, 6, 1, 5, 2 ]
vertex  6 -> Algebra 1464    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  506    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1020

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 2, 4, 5, 3 ] 
[ 1, 2, 4 ] 
[ 5, 3, 2, 4 ] 
[ 3, 2, 4, 5 ] 
[ 2, 8, 6 ] 
[ 1, 2, 8 ] 
[ 6, 2, 8 ] 
[ 2, 4, 1 ] - [ 2, 8, 1 ] 
[ 4, 1, 2 ] - [ 4, 5, 3, 2 ] 
[ 8, 1, 2 ] - [ 8, 6, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(1 1 0 1 1 0 0 1)
(1 1 1 1 0 0 0 1)
(1 1 1 1 1 0 0 0)
(0 1 1 0 1 0 0 1)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1322    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  506    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1466    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1030    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1315    permutation [ 3, 4, 6, 8, 7, 1, 5, 2 ]
vertex  7 -> Algebra 1418    permutation [ 3, 4, 8, 7, 6, 1, 5, 2 ]

Algebra 1023

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 7, 4, 2 ] 
[ 8, 2, 3 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 4, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 4, 2, 3 ] - [ 4, 6, 3 ] 
[ 2, 3, 4 ] - [ 2, 7, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 0 1 0)
(1 1 1 1 0 0 0 1)
(1 1 1 1 0 1 0 0)
(0 0 1 0 1 1 0 1)
(0 0 1 0 0 1 0 1)
(0 0 0 1 0 1 1 0)
(1 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra  828    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1468    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  763    permutation [ 4, 2, 1, 3, 8, 6, 5, 7 ]
vertex  6 -> Algebra 1017    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]

Algebra 1030

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 5, 3 ] 
[ 2, 4, 5 ] 
[ 3, 4, 5 ] 
[ 4, 8, 6 ] 
[ 1, 2, 4, 8 ] 
[ 6, 4, 8 ] 
[ 4, 5, 2 ] - [ 4, 8, 1, 2 ] 
[ 5, 2, 4 ] - [ 5, 3, 4 ] 
[ 8, 1, 2, 4 ] - [ 8, 6, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1332    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1020    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1376    permutation [ 1, 4, 3, 5, 8, 6, 7, 2 ]
vertex  6 -> Algebra 1187    permutation [ 1, 3, 4, 5, 6, 8, 7, 2 ]
vertex  7 -> Algebra 1194    permutation [ 1, 3, 4, 5, 8, 7, 6, 2 ]

Algebra 1048

Quiver

[ 2, 1 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 6 ], [ 6, 7 ], [ 7, 2 ], [ 8, 3 ]

Relations

[ 8, 3, 5, 6, 7, 2 ] 
[ 4, 8, 3 ] 
[ 5, 6, 7, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 7, 2, 8, 3, 5 ] 
[ 7, 2, 8, 3, 5, 6 ] 
[ 2, 8, 3, 5, 6, 7 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 7, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 0 0 0 1)
(1 1 0 0 1 1 1 1)
(1 1 1 0 0 1 1 1)
(1 1 1 0 1 0 1 1)
(0 0 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  871    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1273    permutation [ 6, 8, 1, 2, 3, 4, 5, 7 ]
vertex  5 -> Algebra  756    permutation [ 6, 2, 1, 8, 3, 4, 5, 7 ]

Algebra 1054

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 5, 8 ], [ 6, 3 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 5, 1 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 2, 5 ] 
[ 6, 3, 5 ] 
[ 3, 5, 6 ] 
[ 2, 5, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 2 ] 
[ 5, 6, 3 ] - [ 5, 8, 3 ] 
[ 8, 2, 5 ] - [ 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 1 0 0)
(1 1 1 1 1 0 0 1)
(0 1 0 1 0 0 0 1)
(1 1 1 0 1 1 0 1)
(0 0 1 1 0 1 0 0)
(0 1 0 0 1 1 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra  531    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1002    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  936    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1479    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1055

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 5 ], [ 3, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 7, 5, 2 ] 
[ 8, 2, 3 ] 
[ 6, 3, 5 ] 
[ 3, 5, 6 ] 
[ 5, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 5, 2 ] - [ 3, 8, 2 ] 
[ 5, 2, 3 ] - [ 5, 6, 3 ] 
[ 2, 3, 5 ] - [ 2, 7, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 0 1 0)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 1 1 0 1 1 0 0)
(0 0 1 1 0 1 0 1)
(0 0 0 0 1 1 1 0)
(1 1 0 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra  878    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1480    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1261    permutation [ 5, 2, 1, 3, 4, 8, 6, 7 ]
vertex  8 -> Algebra  531    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1113

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 3, 1 ], [ 3, 8 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 6, 4 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 4, 8, 6 ] 
[ 6, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 2 ] 
[ 4, 5, 2 ] - [ 4, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 6, 4 ] 
[ 2, 3, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 1 1 1 0 1 1 1)
(0 1 0 1 1 0 0 1)
(0 1 1 0 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 0 1 1 1)

Good mutations

vertex  6 -> Algebra 1394    permutation [ 1, 3, 4, 5, 6, 8, 7, 2 ]
vertex  7 -> Algebra 1191    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1376    permutation [ 1, 8, 4, 5, 3, 6, 7, 2 ]

Algebra 1166

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 7 ], [ 7, 1 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 6, 7, 1 ] 
[ 5, 3, 4 ] 
[ 6, 7, 1, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 7, 1, 8, 3, 4, 6 ] 
[ 1, 8, 3, 4, 6, 7 ] 
[ 3, 4, 6, 7, 1, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 7, 1, 8, 3 ] 

Cartan matrix

(1 0 1 1 0 1 0 1)
(1 1 1 1 0 1 1 0)
(1 0 1 1 0 1 1 0)
(1 0 1 1 1 1 1 1)
(0 0 1 0 1 0 0 0)
(1 0 1 0 0 1 1 1)
(1 0 1 1 0 0 1 1)
(0 0 1 1 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1256    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1224    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1167    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  798    permutation [ 2, 3, 4, 6, 7, 1, 8, 5 ]

Algebra 1167

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 7, 4 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 6, 1 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 8, 3, 4, 6 ] 
[ 7, 4, 6 ] 
[ 4, 6, 7 ] 
[ 3, 4, 6, 1, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 1, 8, 3 ] 
[ 6, 1, 8, 3, 4 ] - [ 6, 7, 4 ] 

Cartan matrix

(1 0 1 1 0 0 0 1)
(1 1 1 1 0 1 0 0)
(1 0 1 1 0 1 0 0)
(1 0 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(1 0 1 1 0 1 1 1)
(0 0 0 1 1 0 1 0)
(0 0 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1319    permutation [ 2, 3, 4, 6, 7, 8, 1, 5 ]
vertex  2 -> Algebra 1257    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1225    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  821    permutation [ 2, 3, 4, 6, 7, 1, 8, 5 ]
vertex  7 -> Algebra 1166    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  822    permutation [ 2, 3, 4, 6, 7, 1, 8, 5 ]

Algebra 1168

Quiver

[ 1, 6 ], [ 2, 4 ], [ 2, 8 ], [ 3, 1 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 8 ], [ 6, 4 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 4, 3, 1 ] 
[ 4, 3, 2 ] 
[ 8, 3, 2 ] 
[ 1, 6, 4, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 5 ] 
[ 4, 3, 1, 6 ] 
[ 2, 4, 3 ] - [ 2, 8, 3 ] 
[ 3, 1, 6, 4 ] - [ 3, 2, 4 ] 
[ 3, 2, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 0 0 1 0 1 1 0)
(1 1 1 1 0 0 0 1)
(1 1 1 1 1 1 1 1)
(1 0 1 1 1 0 0 0)
(0 0 0 0 1 0 0 1)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1339    permutation [ 2, 1, 4, 3, 6, 7, 8, 5 ]
vertex  2 -> Algebra 1504    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  657    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  724    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1248    permutation [ 1, 2, 8, 5, 3, 6, 7, 4 ]
vertex  6 -> Algebra 1280    permutation [ 3, 2, 1, 7, 6, 8, 5, 4 ]
vertex  7 -> Algebra 1326    permutation [ 2, 3, 4, 1, 7, 6, 8, 5 ]

Algebra 1171

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 1 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 4 ], [ 8, 1 ]

Relations

[ 7, 4, 1 ] 
[ 8, 1, 3 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 4, 1, 7 ] 
[ 1, 3, 8 ] 
[ 3, 4, 1 ] - [ 3, 8, 1 ] 
[ 4, 1, 3 ] - [ 4, 6, 3 ] 
[ 1, 3, 4 ] - [ 1, 7, 4 ] 

Cartan matrix

(1 0 1 1 0 0 1 0)
(1 1 1 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 0 1 1 0 1 0 0)
(0 0 1 0 1 1 0 1)
(0 0 1 0 0 1 0 1)
(0 0 0 1 0 1 1 0)
(1 0 0 0 0 0 1 1)

Good mutations

vertex  2 -> Algebra 1261    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1278    permutation [ 6, 2, 1, 7, 4, 8, 5, 3 ]
vertex  5 -> Algebra  878    permutation [ 2, 3, 4, 5, 1, 7, 8, 6 ]
vertex  6 -> Algebra  804    permutation [ 2, 3, 6, 4, 1, 7, 8, 5 ]

Algebra 1186

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 3 ], [ 3, 5 ], [ 3, 8 ], [ 4, 2 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 7, 6, 1 ] 
[ 3, 8, 4, 2 ] 
[ 5, 6, 1, 3 ] 
[ 2, 3, 8, 4 ] 
[ 6, 1, 3, 5 ] 
[ 6, 1, 7 ] 
[ 1, 3, 8 ] 
[ 4, 2, 3, 8 ] 
[ 3, 5, 6, 1 ] - [ 3, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 4, 2, 3 ] 
[ 1, 3, 5, 6 ] - [ 1, 7, 6 ] 

Cartan matrix

(1 0 1 0 1 1 1 0)
(1 1 1 0 1 1 0 1)
(1 0 1 1 1 1 0 1)
(0 1 1 1 1 1 0 0)
(1 0 0 0 1 1 0 0)
(1 0 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1273    permutation [ 2, 1, 5, 6, 8, 7, 4, 3 ]
vertex  2 -> Algebra 1365    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  803    permutation [ 2, 8, 5, 6, 1, 7, 4, 3 ]
vertex  8 -> Algebra  678    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1187

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 8 ], [ 5, 6 ], [ 6, 1 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 8, 3, 5, 6, 1 ] 
[ 3, 4, 2 ] 
[ 5, 6, 1, 8, 3 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 1, 8, 3, 5, 6 ] 
[ 7, 5, 6 ] 
[ 5, 6, 7 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 6, 1, 8, 3, 5 ] - [ 6, 7, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 1, 8 ] 

Cartan matrix

(1 0 1 0 1 0 0 1)
(1 1 1 0 1 1 0 0)
(1 0 1 1 1 1 0 1)
(0 1 1 1 1 1 0 1)
(1 0 0 0 1 1 0 1)
(1 0 1 0 1 1 1 1)
(0 0 0 0 1 0 1 0)
(0 0 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1318    permutation [ 2, 4, 5, 6, 7, 8, 1, 3 ]
vertex  2 -> Algebra 1366    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1203    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra  821    permutation [ 2, 4, 5, 6, 7, 1, 8, 3 ]
vertex  5 -> Algebra 1030    permutation [ 1, 8, 2, 3, 4, 5, 7, 6 ]
vertex  8 -> Algebra 1315    permutation [ 2, 8, 5, 6, 7, 1, 4, 3 ]

Algebra 1191

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 8 ], [ 5, 6 ], [ 5, 8 ], [ 6, 3 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 5, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 6, 3, 5 ] 
[ 3, 5, 6 ] 
[ 1, 5, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 5, 6, 3 ] - [ 5, 8, 3 ] 
[ 8, 1, 5 ] - [ 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 1 0 0)
(0 1 1 0 1 0 0 0)
(0 0 1 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 1 0 1 1 0 1)
(0 0 1 1 0 1 0 0)
(1 0 0 0 1 1 1 0)
(1 0 1 0 1 0 0 1)

Good mutations

vertex  7 -> Algebra 1113    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1373    permutation [ 2, 8, 5, 6, 4, 7, 1, 3 ]

Algebra 1194

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 8 ], [ 5, 1 ], [ 5, 7 ], [ 6, 7 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 8, 3, 5, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 1, 8, 3, 5 ] 
[ 7, 3, 5 ] 
[ 3, 5, 7 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 5, 1, 8, 3 ] - [ 5, 7, 3 ] 
[ 3, 4, 8 ] - [ 3, 5, 1, 8 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(1 1 1 0 1 0 0 0)
(1 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(1 0 1 0 1 0 1 1)
(0 0 1 1 0 1 1 0)
(0 0 1 1 0 0 1 0)
(0 0 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1419    permutation [ 2, 4, 5, 6, 7, 8, 1, 3 ]
vertex  2 -> Algebra 1373    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1030    permutation [ 1, 8, 2, 3, 4, 7, 6, 5 ]
vertex  8 -> Algebra 1418    permutation [ 2, 8, 5, 6, 7, 1, 4, 3 ]

Algebra 1201

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 2 ], [ 5, 8 ], [ 6, 7 ], [ 7, 1 ], [ 8, 3 ]

Relations

[ 8, 3, 6, 7, 1 ] 
[ 3, 5, 2 ] 
[ 6, 7, 1, 8, 3 ] 
[ 2, 3, 5 ] 
[ 8, 3, 5 ] 
[ 7, 1, 8, 3, 6 ] 
[ 1, 8, 3, 6, 7 ] 
[ 5, 2, 3 ] - [ 5, 8, 3 ] 
[ 3, 5, 8 ] - [ 3, 6, 7, 1, 8 ] 

Cartan matrix

(1 0 1 0 0 1 0 1)
(1 1 1 0 0 1 1 0)
(1 0 1 0 1 1 1 1)
(0 1 1 1 1 1 1 1)
(0 1 1 0 1 1 1 1)
(1 0 0 0 0 1 1 1)
(1 0 1 0 0 0 1 1)
(0 0 1 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1414    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1224    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1203    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1313    permutation [ 8, 2, 1, 6, 7, 5, 4, 3 ]

Algebra 1203

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 2 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 8, 3, 6, 1 ] 
[ 3, 5, 2 ] 
[ 2, 3, 5 ] 
[ 8, 3, 5 ] 
[ 1, 8, 3, 6 ] 
[ 7, 3, 6 ] 
[ 3, 6, 7 ] 
[ 5, 2, 3 ] - [ 5, 8, 3 ] 
[ 6, 1, 8, 3 ] - [ 6, 7, 3 ] 
[ 3, 5, 8 ] - [ 3, 6, 1, 8 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(1 1 1 0 0 1 0 0)
(1 0 1 0 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 1 1 0 1 1 0 1)
(1 0 1 0 0 1 1 1)
(0 0 1 0 1 0 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1494    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  2 -> Algebra 1415    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1225    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1187    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra 1201    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1468    permutation [ 1, 3, 2, 8, 4, 5, 7, 6 ]

Algebra 1220

Quiver

[ 1, 7 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 6 ], [ 6, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 7, 6, 1 ] 
[ 4, 2, 3 ] 
[ 5, 6, 8, 2, 3 ] 
[ 2, 3, 4 ] 
[ 6, 8, 2, 3, 5 ] 
[ 1, 7, 6 ] 
[ 2, 3, 5, 6, 8 ] 
[ 7, 6, 8 ] 
[ 3, 4, 2 ] - [ 3, 5, 6, 8, 2 ] 
[ 8, 2, 3, 5, 6 ] - [ 8, 7, 6 ] 
[ 6, 1, 7 ] - [ 6, 8, 7 ] 

Cartan matrix

(1 0 0 0 0 0 1 0)
(1 1 1 0 1 1 0 0)
(1 1 1 1 1 1 1 1)
(0 1 0 1 0 0 0 0)
(1 1 0 0 1 1 1 1)
(1 1 1 0 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1366    permutation [ 5, 8, 7, 1, 2, 3, 4, 6 ]
vertex  7 -> Algebra 1016    permutation [ 1, 7, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1281    permutation [ 5, 2, 1, 7, 8, 3, 4, 6 ]

Algebra 1224

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 6, 7 ], [ 7, 1 ], [ 8, 3 ]

Relations

[ 8, 3, 6, 7, 1 ] 
[ 3, 4, 2 ] 
[ 6, 7, 1, 8, 3 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 7, 1, 8, 3, 6 ] 
[ 1, 8, 3, 6, 7 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 3, 4, 8 ] - [ 3, 6, 7, 1, 8 ] 

Cartan matrix

(1 0 1 0 0 1 0 1)
(1 1 1 0 0 1 1 0)
(1 0 1 1 1 1 1 1)
(0 1 1 1 1 1 1 1)
(0 0 0 0 1 0 0 0)
(1 0 0 0 0 1 1 1)
(1 0 1 0 0 0 1 1)
(0 0 1 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1322    permutation [ 8, 3, 1, 6, 7, 4, 5, 2 ]
vertex  4 -> Algebra 1166    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1201    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1225    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  819    permutation [ 8, 2, 1, 6, 7, 4, 5, 3 ]

Algebra 1225

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 6, 1 ], [ 6, 7 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 8, 3, 6, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 1, 8, 3, 6 ] 
[ 7, 3, 6 ] 
[ 3, 6, 7 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 6, 1, 8, 3 ] - [ 6, 7, 3 ] 
[ 3, 4, 8 ] - [ 3, 6, 1, 8 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(1 1 1 0 0 1 0 0)
(1 0 1 1 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(1 0 1 0 0 1 1 1)
(0 0 1 1 1 0 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1490    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  2 -> Algebra 1333    permutation [ 8, 7, 1, 3, 6, 4, 5, 2 ]
vertex  4 -> Algebra 1167    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1203    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra 1224    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1258    permutation [ 8, 3, 1, 2, 6, 4, 5, 7 ]

Algebra 1236

Quiver

[ 1, 7 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 3 ], [ 7, 4 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 7, 4, 1 ] 
[ 3, 4, 8, 2 ] 
[ 1, 7, 4 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 2, 3, 4, 8 ] 
[ 7, 4, 8 ] 
[ 4, 6, 3 ] - [ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] - [ 8, 7, 4 ] 
[ 4, 1, 7 ] - [ 4, 8, 7 ] 

Cartan matrix

(1 0 0 0 0 0 1 0)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 1 1)
(1 1 1 1 0 1 1 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 0 0 1 0 1 1 0)
(0 1 1 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1363    permutation [ 6, 8, 7, 1, 2, 3, 5, 4 ]
vertex  2 -> Algebra 1272    permutation [ 6, 8, 1, 7, 3, 2, 5, 4 ]
vertex  5 -> Algebra 1242    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  784    permutation [ 6, 8, 1, 7, 2, 3, 5, 4 ]
vertex  8 -> Algebra 1278    permutation [ 6, 2, 1, 7, 8, 3, 5, 4 ]

Algebra 1238

Quiver

[ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 5 ], [ 4, 8 ], [ 5, 1 ], [ 6, 4 ], [ 6, 7 ], [ 8, 1 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 3, 8, 1 ] 
[ 3, 8, 2 ] 
[ 5, 1, 4 ] 
[ 1, 4, 5 ] 
[ 4, 8, 6 ] 
[ 2, 3, 8 ] 
[ 6, 4, 8 ] 
[ 4, 5, 1 ] - [ 4, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 2, 3 ] 
[ 8, 1, 4 ] - [ 8, 6, 4 ] 
[ 1, 3, 8 ] - [ 1, 4, 8 ] 

Cartan matrix

(1 0 1 1 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 0 0 1 1 1)
(1 1 1 1 1 0 0 1)
(1 0 1 0 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1239    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1242    permutation [ 2, 5, 4, 8, 6, 7, 3, 1 ]
vertex  6 -> Algebra 1439    permutation [ 2, 4, 5, 6, 8, 7, 3, 1 ]
vertex  7 -> Algebra 1272    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]

Algebra 1239

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 4, 8, 6, 1 ] 
[ 3, 4, 8, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 4, 8, 6 ] 
[ 2, 3, 4, 8 ] 
[ 6, 1, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] - [ 8, 6, 1, 4 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(0 1 1 1 0 0 0 0)
(0 0 1 1 0 1 1 1)
(0 1 1 1 1 1 1 1)
(0 0 1 0 1 0 0 0)
(1 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra  724    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1238    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1246    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1365    permutation [ 4, 8, 7, 6, 2, 3, 5, 1 ]
vertex  7 -> Algebra 1295    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1339    permutation [ 2, 1, 8, 4, 6, 7, 3, 5 ]

Algebra 1242

Quiver

[ 1, 7 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 4 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 7, 4, 1 ] 
[ 3, 4, 8, 2 ] 
[ 1, 7, 4 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 3, 4, 8 ] 
[ 7, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] - [ 8, 7, 4 ] 
[ 4, 1, 7 ] - [ 4, 8, 7 ] 

Cartan matrix

(1 0 0 0 0 0 1 0)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 1 1)
(1 1 1 1 1 1 1 1)
(0 0 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 1 1 1 1 0)
(0 1 1 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1443    permutation [ 8, 7, 1, 2, 3, 5, 6, 4 ]
vertex  2 -> Algebra 1238    permutation [ 8, 1, 7, 3, 2, 5, 6, 4 ]
vertex  6 -> Algebra 1236    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1245    permutation [ 2, 1, 7, 8, 3, 5, 6, 4 ]

Algebra 1245

Quiver

[ 1, 4 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 4, 8, 1 ] 
[ 5, 8, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 5, 8, 6 ] 
[ 2, 3, 4, 8 ] 
[ 6, 5, 8 ] 
[ 8, 1, 4 ] - [ 8, 2, 3, 4 ] 
[ 8, 1, 5 ] - [ 8, 6, 5 ] 
[ 1, 4, 8 ] - [ 1, 5, 8 ] 

Cartan matrix

(1 1 0 1 1 0 0 1)
(0 1 1 1 0 0 0 0)
(0 0 1 1 0 1 1 1)
(0 1 0 1 0 1 1 1)
(0 1 1 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1246    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  2 -> Algebra 1404    permutation [ 1, 2, 4, 7, 8, 3, 5, 6 ]
vertex  4 -> Algebra 1242    permutation [ 2, 1, 5, 8, 6, 7, 3, 4 ]
vertex  7 -> Algebra 1278    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra  878    permutation [ 1, 8, 4, 7, 2, 3, 5, 6 ]

Algebra 1246

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 5, 8, 6, 1 ] 
[ 3, 4, 5, 8, 2 ] 
[ 4, 5, 8, 2, 3 ] 
[ 5, 8, 2, 3, 4 ] 
[ 1, 5, 8, 6 ] 
[ 2, 3, 4, 5, 8 ] 
[ 6, 1, 5, 8 ] 
[ 8, 2, 3, 4, 5 ] - [ 8, 6, 1, 5 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 0 1 1 1 1 1 1)
(0 1 0 1 1 1 1 1)
(0 1 1 0 1 1 1 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  738    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1444    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1239    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1245    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1283    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1480    permutation [ 8, 5, 4, 7, 2, 3, 1, 6 ]

Algebra 1248

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 2 ], [ 6, 7 ], [ 6, 8 ], [ 8, 5 ]

Relations

[ 6, 8, 5, 1 ] 
[ 3, 4, 5, 2 ] 
[ 8, 5, 2 ] 
[ 4, 5, 2, 3 ] 
[ 5, 2, 3, 4 ] 
[ 1, 6, 8, 5 ] 
[ 8, 5, 1, 6 ] 
[ 2, 3, 4, 5 ] - [ 2, 8, 5 ] 
[ 5, 1, 6, 8 ] - [ 5, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 1 1 1)
(1 1 1 1 1 0 0 1)
(1 0 1 1 1 1 1 0)
(1 1 0 1 1 1 1 1)
(1 1 1 0 1 1 1 1)
(0 0 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1480    permutation [ 8, 5, 4, 7, 2, 3, 1, 6 ]
vertex  2 -> Algebra 1522    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1168    permutation [ 1, 2, 5, 8, 4, 6, 7, 3 ]
vertex  6 -> Algebra 1296    permutation [ 2, 4, 8, 6, 1, 7, 3, 5 ]
vertex  7 -> Algebra 1325    permutation [ 2, 4, 8, 1, 7, 6, 3, 5 ]
vertex  8 -> Algebra  738    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1256

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 2 ], [ 6, 7 ], [ 7, 1 ], [ 8, 2 ]

Relations

[ 8, 2, 4, 6, 7, 1 ] 
[ 5, 2, 4 ] 
[ 6, 7, 1, 8, 2, 4 ] 
[ 2, 4, 5 ] 
[ 7, 1, 8, 2, 4, 6 ] 
[ 1, 8, 2, 4, 6, 7 ] 
[ 2, 4, 6, 7, 1, 8 ] 
[ 4, 5, 2 ] - [ 4, 6, 7, 1, 8, 2 ] 

Cartan matrix

(1 1 1 1 0 1 0 1)
(1 1 1 1 0 1 1 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 1 1 1 1)
(0 1 1 0 1 0 0 0)
(1 1 1 0 0 1 1 1)
(1 1 1 1 0 0 1 1)
(0 1 1 1 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1311    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1166    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1257    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  998    permutation [ 3, 2, 4, 6, 7, 1, 8, 5 ]

Algebra 1257

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 2 ], [ 6, 1 ], [ 6, 7 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 8, 2, 4, 6, 1 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 1, 8, 2, 4, 6 ] 
[ 7, 4, 6 ] 
[ 4, 6, 7 ] 
[ 2, 4, 6, 1, 8 ] 
[ 4, 5, 2 ] - [ 4, 6, 1, 8, 2 ] 
[ 6, 1, 8, 2, 4 ] - [ 6, 7, 4 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(1 1 1 1 0 1 0 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 1 1 0 1 0 0 0)
(1 1 1 1 0 1 1 1)
(0 0 0 1 1 0 1 0)
(0 1 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1464    permutation [ 3, 2, 4, 6, 7, 8, 1, 5 ]
vertex  2 -> Algebra 1312    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1167    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1016    permutation [ 3, 2, 4, 6, 7, 1, 8, 5 ]
vertex  7 -> Algebra 1256    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1017    permutation [ 3, 2, 4, 6, 7, 1, 8, 5 ]

Algebra 1258

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 3, 2 ], [ 4, 2 ], [ 5, 3 ], [ 5, 8 ], [ 6, 4 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 3, 2, 1 ] 
[ 6, 4, 2, 1 ] 
[ 2, 1, 6, 4 ] 
[ 3, 2, 5 ] 
[ 8, 2, 5 ] 
[ 4, 2, 1, 6 ] 
[ 2, 5, 8 ] 
[ 1, 3, 2 ] - [ 1, 6, 4, 2 ] 
[ 5, 3, 2 ] - [ 5, 8, 2 ] 
[ 2, 1, 3 ] - [ 2, 5, 3 ] 

Cartan matrix

(1 1 1 1 0 1 1 0)
(1 1 1 0 1 1 1 0)
(0 1 1 0 0 0 0 0)
(1 1 1 1 1 0 0 0)
(0 1 1 0 1 0 0 1)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1225    permutation [ 3, 4, 2, 6, 7, 5, 8, 1 ]
vertex  2 -> Algebra  763    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1504    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  836    permutation [ 1, 8, 3, 2, 5, 6, 7, 4 ]
vertex  6 -> Algebra 1317    permutation [ 4, 1, 2, 5, 8, 3, 6, 7 ]
vertex  7 -> Algebra 1468    permutation [ 3, 2, 4, 1, 7, 6, 8, 5 ]
vertex  8 -> Algebra  819    permutation [ 1, 4, 3, 8, 5, 6, 7, 2 ]

Algebra 1261

Quiver

[ 1, 2 ], [ 1, 7 ], [ 2, 3 ], [ 2, 4 ], [ 2, 8 ], [ 4, 1 ], [ 4, 6 ], [ 5, 6 ], [ 6, 2 ], [ 7, 4 ], [ 8, 1 ]

Relations

[ 7, 4, 1 ] 
[ 8, 1, 2 ] 
[ 6, 2, 4 ] 
[ 2, 4, 6 ] 
[ 4, 1, 7 ] 
[ 1, 2, 8 ] 
[ 2, 4, 1 ] - [ 2, 8, 1 ] 
[ 4, 1, 2 ] - [ 4, 6, 2 ] 
[ 1, 2, 4 ] - [ 1, 7, 4 ] 

Cartan matrix

(1 1 1 1 0 0 1 0)
(1 1 1 1 0 0 0 1)
(0 0 1 0 0 0 0 0)
(1 1 1 1 0 1 0 0)
(0 1 1 0 1 1 0 1)
(0 1 1 0 0 1 0 1)
(0 0 0 1 0 1 1 0)
(1 0 0 0 0 0 1 1)

Good mutations

vertex  2 -> Algebra 1523    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1171    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1055    permutation [ 3, 2, 4, 5, 1, 7, 8, 6 ]
vertex  6 -> Algebra 1003    permutation [ 3, 2, 6, 4, 1, 7, 8, 5 ]

Algebra 1272

Quiver

[ 1, 5 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 6 ], [ 5, 8 ], [ 6, 2 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 5, 8, 1 ] 
[ 4, 8, 2 ] 
[ 4, 8, 3 ] 
[ 6, 2, 5 ] 
[ 2, 5, 6 ] 
[ 1, 5, 8 ] 
[ 3, 4, 8 ] 
[ 5, 6, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 8, 1, 5 ] - [ 8, 2, 5 ] 
[ 2, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 1 0 0)
(0 1 0 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 1 1 1 1 1 0 1)
(0 1 0 1 0 1 0 0)
(1 0 0 0 1 1 1 0)
(1 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  786    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1295    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1236    permutation [ 3, 6, 5, 8, 7, 1, 4, 2 ]
vertex  7 -> Algebra 1238    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]

Algebra 1273

Quiver

[ 1, 8 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 6 ], [ 5, 7 ], [ 6, 2 ], [ 7, 1 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 5, 7, 1 ] 
[ 4, 8, 2 ] 
[ 4, 8, 3 ] 
[ 6, 2, 5 ] 
[ 7, 1, 8, 2, 5 ] 
[ 2, 5, 6 ] 
[ 1, 8, 2, 5, 7 ] 
[ 3, 4, 8 ] 
[ 5, 6, 2 ] - [ 5, 7, 1, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 4, 8 ] - [ 2, 5, 7, 1, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(1 1 0 1 1 0 1 1)
(0 0 1 1 0 0 0 0)
(0 0 0 1 0 0 0 1)
(1 1 1 1 1 1 1 1)
(0 1 0 1 0 1 0 0)
(1 1 1 1 0 0 1 1)
(0 1 1 1 1 0 1 1)

Good mutations

vertex  1 -> Algebra 1439    permutation [ 3, 5, 6, 7, 8, 1, 4, 2 ]
vertex  2 -> Algebra 1186    permutation [ 2, 1, 8, 7, 3, 4, 6, 5 ]
vertex  4 -> Algebra 1048    permutation [ 3, 4, 5, 6, 7, 1, 8, 2 ]
vertex  7 -> Algebra  786    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1278

Quiver

[ 1, 6 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 8, 1 ] 
[ 5, 8, 2 ] 
[ 6, 8, 2 ] 
[ 4, 5, 8, 3 ] 
[ 5, 8, 3, 4 ] 
[ 1, 6, 8 ] 
[ 3, 4, 5, 8 ] 
[ 8, 2, 5 ] - [ 8, 3, 4, 5 ] 
[ 8, 1, 6 ] - [ 8, 2, 6 ] 
[ 2, 5, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 1 0 1 1 0 1)
(0 0 1 1 1 0 0 0)
(1 0 0 1 1 0 0 1)
(1 0 1 0 1 0 0 1)
(0 0 1 1 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  793    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1283    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1383    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1236    permutation [ 3, 2, 6, 8, 7, 1, 4, 5 ]
vertex  7 -> Algebra 1245    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1171    permutation [ 3, 2, 8, 5, 7, 1, 4, 6 ]

Algebra 1280

Quiver

[ 1, 2 ], [ 1, 3 ], [ 1, 7 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 3, 8, 1 ] 
[ 7, 6, 1 ] 
[ 6, 1, 2 ] 
[ 8, 1, 2 ] 
[ 4, 5, 3 ] 
[ 5, 3, 4 ] 
[ 6, 1, 7 ] 
[ 5, 3, 8 ] 
[ 2, 6, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 5, 3 ] 
[ 3, 4, 5 ] - [ 3, 8, 5 ] 
[ 1, 2, 6 ] - [ 1, 7, 6 ] 
[ 1, 2, 8 ] - [ 1, 3, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 0 1 1 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 1 0 1 0 0 0)
(1 0 1 1 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 1 0 1 0 1 1)

Good mutations

vertex  1 -> Algebra  804    permutation [ 2, 1, 8, 5, 3, 4, 6, 7 ]
vertex  2 -> Algebra 1323    permutation [ 8, 1, 2, 7, 6, 3, 5, 4 ]
vertex  3 -> Algebra 1300    permutation [ 2, 3, 8, 5, 1, 4, 6, 7 ]
vertex  4 -> Algebra 1286    permutation [ 2, 1, 8, 5, 4, 3, 6, 7 ]
vertex  5 -> Algebra 1168    permutation [ 3, 2, 1, 8, 7, 5, 4, 6 ]
vertex  7 -> Algebra 1296    permutation [ 2, 7, 8, 5, 3, 4, 6, 1 ]
vertex  8 -> Algebra  793    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1281

Quiver

[ 1, 8 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 6, 1 ] 
[ 5, 8, 2 ] 
[ 4, 5, 8, 3 ] 
[ 5, 8, 3, 4 ] 
[ 1, 8, 2, 6 ] 
[ 7, 2, 6 ] 
[ 2, 6, 7 ] 
[ 3, 4, 5, 8 ] 
[ 6, 1, 8, 2 ] - [ 6, 7, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 4, 5 ] 
[ 2, 5, 8 ] - [ 2, 6, 1, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(1 1 1 0 1 1 0 1)
(0 0 1 1 1 0 0 0)
(0 0 0 1 1 0 0 1)
(0 0 1 0 1 0 0 1)
(1 1 1 1 1 1 1 1)
(0 1 0 0 1 0 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1288    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1386    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1312    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1220    permutation [ 3, 2, 6, 7, 1, 8, 4, 5 ]

Algebra 1283

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 6, 8, 1 ] 
[ 6, 8, 1, 2 ] 
[ 4, 5, 6, 8, 3 ] 
[ 5, 6, 8, 3, 4 ] 
[ 6, 8, 3, 4, 5 ] 
[ 1, 2, 6, 8 ] 
[ 3, 4, 5, 6, 8 ] 
[ 8, 1, 2, 6 ] - [ 8, 3, 4, 5, 6 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(0 1 1 1 0 1 0 1)
(0 0 1 1 1 1 0 0)
(1 0 0 1 1 1 0 1)
(1 0 1 0 1 1 0 1)
(1 0 1 1 0 1 0 1)
(1 1 0 0 0 1 1 0)
(1 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  796    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  996    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1390    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1295    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra 1278    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1246    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1523    permutation [ 3, 6, 8, 5, 7, 1, 4, 2 ]

Algebra 1285

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 3, 8, 1 ] 
[ 7, 2, 8, 1 ] 
[ 8, 1, 7, 2 ] 
[ 4, 5, 6, 3 ] 
[ 5, 6, 3, 4 ] 
[ 6, 3, 4, 5 ] 
[ 2, 8, 1, 7 ] 
[ 6, 3, 8 ] 
[ 8, 1, 3 ] - [ 8, 6, 3 ] 
[ 3, 4, 5, 6 ] - [ 3, 8, 6 ] 
[ 1, 3, 8 ] - [ 1, 7, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 1 0 1 0 1)
(0 0 1 1 1 1 0 1)
(0 0 0 1 1 1 0 0)
(0 0 1 0 1 1 0 0)
(0 0 1 1 0 1 0 0)
(0 1 0 0 0 1 1 1)
(1 0 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1526    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1286    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1311    permutation [ 8, 1, 6, 4, 5, 7, 2, 3 ]
vertex  4 -> Algebra 1316    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1296    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra 1323    permutation [ 6, 1, 8, 7, 2, 3, 5, 4 ]
vertex  7 -> Algebra 1525    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  796    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1286

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 7 ]

Relations

[ 3, 2, 1 ] 
[ 7, 2, 1 ] 
[ 6, 3, 2 ] 
[ 8, 7, 2 ] 
[ 4, 5, 6, 3 ] 
[ 5, 6, 3, 4 ] 
[ 6, 3, 4, 5 ] 
[ 7, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 7, 2 ] 
[ 2, 1, 3 ] - [ 2, 6, 3 ] 
[ 3, 2, 6 ] - [ 3, 4, 5, 6 ] 
[ 2, 1, 7 ] - [ 2, 8, 7 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 1 1 0 1 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 1 1 1 0 0)
(0 0 1 0 1 1 0 0)
(0 0 1 1 0 1 0 0)
(0 1 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1527    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  798    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1317    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1280    permutation [ 2, 1, 6, 5, 4, 7, 8, 3 ]
vertex  6 -> Algebra 1293    permutation [ 6, 1, 2, 8, 7, 3, 5, 4 ]
vertex  7 -> Algebra  819    permutation [ 2, 1, 6, 4, 5, 7, 8, 3 ]
vertex  8 -> Algebra 1285    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1288

Quiver

[ 1, 8 ], [ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 6, 8 ], [ 7, 5 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 1 ] 
[ 1, 8, 2 ] 
[ 6, 8, 2 ] 
[ 4, 5, 6, 8, 3 ] 
[ 5, 6, 8, 3, 4 ] 
[ 7, 5, 6 ] 
[ 5, 6, 7 ] 
[ 3, 4, 5, 6, 8 ] 
[ 6, 7, 5 ] - [ 6, 8, 3, 4, 5 ] 
[ 8, 2, 6 ] - [ 8, 3, 4, 5, 6 ] 
[ 2, 1, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 0 1 1 1 0 0 1)
(1 1 1 1 1 1 1 1)
(0 0 1 1 1 1 0 0)
(0 0 0 1 1 1 0 1)
(0 0 1 0 1 1 0 1)
(0 0 1 1 1 1 1 1)
(0 0 0 0 1 0 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra  799    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1394    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1318    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1281    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]

Algebra 1293

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 5 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 6, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 7 ]

Relations

[ 3, 2, 6, 1 ] 
[ 7, 6, 1 ] 
[ 5, 3, 2 ] 
[ 6, 1, 3, 2 ] 
[ 4, 5, 3 ] 
[ 5, 3, 4 ] 
[ 8, 7, 6 ] 
[ 7, 6, 8 ] 
[ 2, 5, 3 ] - [ 2, 6, 1, 3 ] 
[ 3, 2, 5 ] - [ 3, 4, 5 ] 
[ 1, 3, 2, 6 ] - [ 1, 7, 6 ] 
[ 6, 1, 7 ] - [ 6, 8, 7 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 1 0 1 1 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 1 1 0 0 0)
(0 0 1 0 1 0 0 0)
(1 0 1 1 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1286    permutation [ 2, 3, 6, 8, 7, 1, 5, 4 ]
vertex  2 -> Algebra 1286    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  4 -> Algebra 1323    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1306    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1306    permutation [ 2, 7, 6, 8, 1, 3, 5, 4 ]
vertex  8 -> Algebra 1323    permutation [ 2, 1, 6, 7, 8, 3, 5, 4 ]

Algebra 1295

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 5, 8, 1 ] 
[ 5, 8, 1, 2 ] 
[ 4, 5, 8, 3 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 1, 2, 5, 8 ] 
[ 3, 4, 5, 8 ] 
[ 5, 6, 4 ] - [ 5, 8, 3, 4 ] 
[ 8, 1, 2, 5 ] - [ 8, 3, 4, 5 ] 

Cartan matrix

(1 1 0 0 1 1 0 0)
(0 1 1 1 1 1 0 1)
(0 0 1 1 1 0 0 0)
(1 0 0 1 1 0 0 1)
(1 0 1 1 1 1 0 1)
(0 0 0 1 0 1 0 0)
(1 1 0 0 1 1 1 0)
(1 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  803    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1002    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1272    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1283    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1239    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1329    permutation [ 3, 2, 8, 5, 7, 1, 4, 6 ]

Algebra 1296

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 2 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 3, 8, 1 ] 
[ 7, 2, 8, 1 ] 
[ 8, 1, 7, 2 ] 
[ 4, 5, 3 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 2, 8, 1, 7 ] 
[ 5, 3, 8 ] 
[ 8, 1, 3 ] - [ 8, 5, 3 ] 
[ 5, 3, 4 ] - [ 5, 6, 4 ] 
[ 3, 4, 5 ] - [ 3, 8, 5 ] 
[ 1, 3, 8 ] - [ 1, 7, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 0 1 1)
(1 1 1 1 1 1 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 1 1 1 1 0 0)
(0 0 0 1 0 1 0 0)
(0 1 0 0 1 1 1 1)
(1 0 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1335    permutation [ 3, 2, 1, 8, 7, 5, 4, 6 ]
vertex  2 -> Algebra 1280    permutation [ 8, 1, 5, 6, 4, 7, 2, 3 ]
vertex  4 -> Algebra 1248    permutation [ 5, 1, 7, 2, 8, 4, 6, 3 ]
vertex  5 -> Algebra 1334    permutation [ 3, 2, 1, 8, 7, 5, 4, 6 ]
vertex  6 -> Algebra 1285    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  803    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1300

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 4 ], [ 2, 5 ], [ 3, 2 ], [ 5, 1 ], [ 5, 6 ], [ 5, 8 ], [ 6, 2 ], [ 7, 5 ], [ 8, 7 ]

Relations

[ 3, 2, 5, 1 ] 
[ 7, 5, 1 ] 
[ 2, 5, 1, 3 ] 
[ 6, 2, 5 ] 
[ 8, 7, 5 ] 
[ 2, 5, 6 ] 
[ 7, 5, 8 ] 
[ 5, 1, 3, 2 ] - [ 5, 6, 2 ] 
[ 1, 3, 2, 5 ] - [ 1, 7, 5 ] 
[ 5, 1, 7 ] - [ 5, 8, 7 ] 

Cartan matrix

(1 1 1 1 1 0 1 0)
(1 1 0 1 1 0 1 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 1 1 1 1 1 1 1)
(0 1 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra  825    permutation [ 3, 5, 1, 8, 7, 2, 4, 6 ]
vertex  2 -> Algebra 1280    permutation [ 5, 1, 2, 6, 4, 7, 8, 3 ]
vertex  3 -> Algebra 1385    permutation [ 5, 1, 6, 3, 4, 7, 8, 2 ]
vertex  4 -> Algebra 1344    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1306    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1334    permutation [ 3, 8, 1, 5, 7, 2, 4, 6 ]

Algebra 1306

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 4 ], [ 2, 5 ], [ 3, 2 ], [ 5, 6 ], [ 6, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 7 ]

Relations

[ 3, 2, 5, 6, 1 ] 
[ 7, 6, 1 ] 
[ 5, 6, 1, 3, 2 ] 
[ 2, 5, 6, 1, 3 ] 
[ 6, 1, 3, 2, 5 ] 
[ 8, 7, 6 ] 
[ 7, 6, 8 ] 
[ 1, 3, 2, 5, 6 ] - [ 1, 7, 6 ] 
[ 6, 1, 7 ] - [ 6, 8, 7 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(1 0 1 0 1 1 1 1)
(1 1 1 1 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra  819    permutation [ 3, 5, 1, 8, 7, 2, 4, 6 ]
vertex  2 -> Algebra 1293    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra 1353    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1300    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1524    permutation [ 6, 1, 2, 5, 4, 7, 8, 3 ]
vertex  8 -> Algebra 1504    permutation [ 3, 6, 1, 5, 7, 2, 4, 8 ]

Algebra 1311

Quiver

[ 1, 8 ], [ 2, 4 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 7 ], [ 7, 1 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 6, 7, 1 ] 
[ 4, 8, 2 ] 
[ 6, 7, 1, 8, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 7, 1, 8, 2, 6 ] 
[ 1, 8, 2, 6, 7 ] 
[ 3, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 4, 8 ] - [ 2, 6, 7, 1, 8 ] 

Cartan matrix

(1 1 1 1 0 1 0 1)
(1 1 1 1 1 1 1 1)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(1 0 1 0 0 1 1 1)
(1 1 1 1 0 0 1 1)
(0 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1392    permutation [ 2, 7, 4, 1, 5, 3, 6, 8 ]
vertex  2 -> Algebra 1315    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1322    permutation [ 8, 2, 1, 6, 7, 3, 5, 4 ]
vertex  4 -> Algebra 1256    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1312    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1285    permutation [ 2, 7, 8, 4, 5, 3, 6, 1 ]

Algebra 1312

Quiver

[ 1, 8 ], [ 2, 4 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 6, 1 ] 
[ 4, 8, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 8, 2, 6 ] 
[ 7, 2, 6 ] 
[ 2, 6, 7 ] 
[ 3, 4, 8 ] 
[ 6, 1, 8, 2 ] - [ 6, 7, 2 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 4, 8 ] - [ 2, 6, 1, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(1 1 1 1 1 1 0 1)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(1 1 1 1 0 1 1 1)
(0 1 0 1 1 0 1 0)
(0 1 1 1 0 1 0 1)

Good mutations

vertex  2 -> Algebra 1318    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1333    permutation [ 8, 7, 1, 2, 6, 3, 5, 4 ]
vertex  4 -> Algebra 1257    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1281    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra 1311    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1525    permutation [ 2, 6, 8, 4, 5, 3, 7, 1 ]

Algebra 1313

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 8 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 3, 8, 1 ] 
[ 6, 2, 8, 1 ] 
[ 8, 1, 6, 2 ] 
[ 5, 3, 8, 4 ] 
[ 3, 8, 4, 5 ] 
[ 2, 8, 1, 6 ] 
[ 4, 5, 3, 8 ] 
[ 8, 1, 3 ] - [ 8, 4, 5, 3 ] 
[ 1, 3, 8 ] - [ 1, 6, 2, 8 ] 

Cartan matrix

(1 1 1 1 0 1 0 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 1 0 1 0 0 1)
(0 1 0 1 1 1 0 1)
(0 1 0 1 1 1 1 1)
(1 0 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1201    permutation [ 3, 2, 8, 7, 6, 4, 5, 1 ]
vertex  2 -> Algebra 1320    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1353    permutation [ 3, 7, 1, 6, 2, 8, 5, 4 ]
vertex  4 -> Algebra 1468    permutation [ 3, 8, 2, 1, 7, 6, 4, 5 ]
vertex  6 -> Algebra 1525    permutation [ 2, 6, 8, 4, 5, 3, 7, 1 ]
vertex  7 -> Algebra  819    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1315

Quiver

[ 1, 8 ], [ 2, 6 ], [ 2, 7 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 8 ], [ 7, 1 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 7, 1 ] 
[ 6, 8, 2 ] 
[ 7, 1, 8, 2 ] 
[ 5, 3, 4 ] 
[ 6, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 8, 2, 7 ] 
[ 3, 4, 6, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 8, 3 ] 
[ 8, 2, 6 ] - [ 8, 3, 4, 6 ] 
[ 2, 6, 8 ] - [ 2, 7, 1, 8 ] 

Cartan matrix

(1 1 1 1 0 1 0 1)
(1 1 1 0 0 1 1 1)
(0 0 1 1 0 1 0 0)
(0 0 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(0 0 1 0 0 1 0 1)
(1 0 1 1 0 0 1 1)
(0 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1516    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  2 -> Algebra 1187    permutation [ 6, 1, 8, 7, 3, 4, 5, 2 ]
vertex  3 -> Algebra 1020    permutation [ 6, 8, 1, 2, 7, 3, 5, 4 ]
vertex  6 -> Algebra 1311    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  8 -> Algebra 1463    permutation [ 6, 3, 1, 2, 7, 8, 5, 4 ]

Algebra 1316

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 3 ], [ 7, 2 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 3, 8, 1 ] 
[ 7, 2, 8, 1 ] 
[ 8, 1, 7, 2 ] 
[ 5, 3, 4 ] 
[ 6, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 8, 1, 7 ] 
[ 6, 3, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 3 ] 
[ 8, 1, 3 ] - [ 8, 6, 3 ] 
[ 3, 4, 6 ] - [ 3, 8, 6 ] 
[ 1, 3, 8 ] - [ 1, 7, 2, 8 ] 

Cartan matrix

(1 1 1 1 0 1 1 1)
(1 1 1 0 0 1 0 1)
(0 0 1 1 0 1 0 1)
(0 0 1 1 1 1 0 0)
(0 0 1 0 1 0 0 1)
(0 0 1 0 0 1 0 0)
(0 1 0 0 0 1 1 1)
(1 0 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1537    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1317    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  998    permutation [ 6, 3, 1, 7, 2, 8, 5, 4 ]
vertex  4 -> Algebra 1325    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra 1285    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1527    permutation [ 3, 6, 1, 7, 2, 8, 5, 4 ]
vertex  7 -> Algebra 1463    permutation [ 6, 3, 1, 2, 7, 8, 5, 4 ]

Algebra 1317

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 3 ], [ 7, 2 ], [ 8, 7 ]

Relations

[ 3, 2, 1 ] 
[ 7, 2, 1 ] 
[ 6, 3, 2 ] 
[ 8, 7, 2 ] 
[ 5, 3, 4 ] 
[ 6, 3, 4 ] 
[ 3, 4, 5 ] 
[ 7, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 7, 2 ] 
[ 2, 1, 3 ] - [ 2, 6, 3 ] 
[ 4, 5, 3 ] - [ 4, 6, 3 ] 
[ 3, 2, 6 ] - [ 3, 4, 6 ] 
[ 2, 1, 7 ] - [ 2, 8, 7 ] 

Cartan matrix

(1 1 1 1 0 1 1 0)
(1 1 1 0 0 1 1 1)
(0 1 1 1 0 1 0 1)
(0 0 1 1 1 1 0 0)
(0 1 1 0 1 0 0 1)
(0 0 1 0 0 1 0 0)
(0 1 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1526    permutation [ 6, 5, 2, 8, 7, 1, 4, 3 ]
vertex  2 -> Algebra  822    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1003    permutation [ 6, 3, 1, 7, 2, 8, 5, 4 ]
vertex  4 -> Algebra 1326    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra 1286    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1323    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1258    permutation [ 2, 3, 6, 1, 4, 7, 8, 5 ]
vertex  8 -> Algebra 1316    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1318

Quiver

[ 1, 8 ], [ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 7 ], [ 6, 8 ], [ 7, 4 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 1 ] 
[ 1, 8, 2 ] 
[ 6, 8, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 7, 4, 6 ] 
[ 4, 6, 7 ] 
[ 3, 4, 6, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 8, 3 ] 
[ 6, 7, 4 ] - [ 6, 8, 3, 4 ] 
[ 8, 2, 6 ] - [ 8, 3, 4, 6 ] 
[ 2, 1, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 0 1 1 0 0 0 1)
(1 1 1 1 0 1 1 1)
(0 0 1 1 0 1 0 0)
(0 0 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(0 0 1 1 0 1 1 1)
(0 0 0 1 1 0 1 0)
(0 1 1 1 0 1 0 1)

Good mutations

vertex  2 -> Algebra  823    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1332    permutation [ 6, 7, 1, 8, 2, 3, 5, 4 ]
vertex  5 -> Algebra 1288    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1312    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1187    permutation [ 7, 1, 8, 2, 3, 4, 5, 6 ]
vertex  8 -> Algebra 1494    permutation [ 1, 3, 2, 8, 4, 5, 7, 6 ]

Algebra 1319

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 8, 2, 3 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 3, 4, 6 ] 
[ 7, 4, 6 ] 
[ 4, 6, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 6, 2 ] - [ 3, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 6, 2, 3 ] 
[ 6, 2, 3, 4 ] - [ 6, 7, 4 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 0)
(0 1 1 1 0 1 0 1)
(0 1 1 1 1 1 0 0)
(0 0 1 0 1 0 0 1)
(0 1 1 1 0 1 1 0)
(0 0 0 1 1 0 1 0)
(0 1 0 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1464    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1490    permutation [ 1, 3, 2, 8, 4, 5, 7, 6 ]
vertex  6 -> Algebra  824    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1167    permutation [ 7, 1, 2, 3, 8, 4, 5, 6 ]
vertex  8 -> Algebra  823    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1320

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 6 ]

Relations

[ 3, 2, 1 ] 
[ 6, 2, 1 ] 
[ 4, 5, 3, 2 ] 
[ 8, 6, 2 ] 
[ 5, 3, 2, 4 ] 
[ 3, 2, 4, 5 ] 
[ 6, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 6, 2 ] 
[ 2, 1, 3 ] - [ 2, 4, 5, 3 ] 
[ 2, 1, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 1 1 0 1 0 0)
(1 1 1 1 1 1 0 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 1 1 0 1 0 0 1)
(0 1 0 1 1 1 0 0)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1414    permutation [ 3, 2, 8, 7, 6, 4, 5, 1 ]
vertex  2 -> Algebra  824    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1344    permutation [ 3, 7, 1, 6, 2, 8, 5, 4 ]
vertex  4 -> Algebra 1331    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1538    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  825    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1313    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1322

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 1 ], [ 4, 5 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 4, 5, 3, 1, 2 ] 
[ 8, 6, 1, 2 ] 
[ 1, 2, 4, 5, 3 ] 
[ 5, 3, 1, 2, 4 ] 
[ 3, 1, 2, 4, 5 ] 
[ 1, 2, 8, 6 ] 
[ 6, 1, 2, 8 ] 
[ 2, 4, 5, 3, 1 ] - [ 2, 8, 6, 1 ] 

Cartan matrix

(1 1 0 1 1 0 0 1)
(1 1 1 1 1 1 1 1)
(1 1 1 1 0 0 0 1)
(1 0 1 1 1 0 0 0)
(1 1 1 0 1 0 0 1)
(1 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  825    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1020    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1539    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1333    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1311    permutation [ 3, 2, 6, 8, 7, 4, 5, 1 ]
vertex  7 -> Algebra 1414    permutation [ 3, 2, 8, 7, 6, 4, 5, 1 ]
vertex  8 -> Algebra 1224    permutation [ 3, 8, 2, 6, 7, 4, 5, 1 ]

Algebra 1323

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 7 ]

Relations

[ 3, 2, 6, 1 ] 
[ 7, 6, 1 ] 
[ 4, 5, 3, 2 ] 
[ 6, 1, 3, 2 ] 
[ 5, 3, 2, 4 ] 
[ 3, 2, 4, 5 ] 
[ 8, 7, 6 ] 
[ 7, 6, 8 ] 
[ 2, 4, 5, 3 ] - [ 2, 6, 1, 3 ] 
[ 1, 3, 2, 6 ] - [ 1, 7, 6 ] 
[ 6, 1, 7 ] - [ 6, 8, 7 ] 

Cartan matrix

(1 1 1 1 0 1 1 0)
(1 1 1 1 1 1 1 1)
(0 1 1 1 0 1 0 1)
(0 0 1 1 1 0 0 0)
(0 1 1 0 1 1 0 1)
(1 0 1 0 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1285    permutation [ 2, 5, 6, 8, 7, 1, 4, 3 ]
vertex  2 -> Algebra 1317    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1280    permutation [ 2, 3, 6, 8, 7, 5, 4, 1 ]
vertex  4 -> Algebra 1335    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1293    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  825    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1504    permutation [ 6, 3, 2, 1, 4, 7, 8, 5 ]
vertex  8 -> Algebra 1527    permutation [ 3, 2, 1, 7, 8, 6, 5, 4 ]

Algebra 1325

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 8 ], [ 3, 8 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 3, 8, 1 ] 
[ 7, 2, 8, 1 ] 
[ 8, 1, 7, 2 ] 
[ 6, 3, 8, 4 ] 
[ 3, 8, 4, 6 ] 
[ 2, 8, 1, 7 ] 
[ 4, 6, 3, 8 ] 
[ 8, 1, 3 ] - [ 8, 4, 6, 3 ] 
[ 1, 3, 8 ] - [ 1, 7, 2, 8 ] 

Cartan matrix

(1 1 1 1 0 0 1 1)
(1 1 1 1 0 1 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 0 1 0 0)
(0 0 1 0 1 1 0 1)
(0 0 1 0 0 1 0 1)
(0 1 0 1 0 1 1 1)
(1 0 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1540    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1326    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  996    permutation [ 4, 6, 1, 7, 2, 8, 5, 3 ]
vertex  4 -> Algebra 1523    permutation [ 1, 8, 3, 2, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1248    permutation [ 4, 1, 7, 2, 8, 6, 5, 3 ]
vertex  6 -> Algebra 1316    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]

Algebra 1326

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 7 ]

Relations

[ 3, 2, 1 ] 
[ 7, 2, 1 ] 
[ 4, 6, 3, 2 ] 
[ 8, 7, 2 ] 
[ 6, 3, 2, 4 ] 
[ 3, 2, 4, 6 ] 
[ 7, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 7, 2 ] 
[ 2, 1, 3 ] - [ 2, 4, 6, 3 ] 
[ 2, 1, 7 ] - [ 2, 8, 7 ] 

Cartan matrix

(1 1 1 1 0 0 1 0)
(1 1 1 1 0 1 1 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 0 1 0 0)
(0 1 1 0 1 1 0 1)
(0 1 1 0 0 1 0 1)
(0 1 0 1 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1541    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  828    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1002    permutation [ 4, 6, 1, 7, 2, 8, 5, 3 ]
vertex  4 -> Algebra 1329    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1168    permutation [ 4, 1, 2, 3, 8, 6, 5, 7 ]
vertex  6 -> Algebra 1317    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  8 -> Algebra 1325    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1329

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 2 ], [ 6, 3 ], [ 7, 4 ], [ 8, 7 ]

Relations

[ 3, 4, 1 ] 
[ 7, 4, 1 ] 
[ 4, 6, 2 ] 
[ 8, 7, 4 ] 
[ 2, 4, 6 ] 
[ 3, 4, 6 ] 
[ 7, 4, 8 ] 
[ 4, 1, 3 ] - [ 4, 6, 3 ] 
[ 1, 3, 4 ] - [ 1, 7, 4 ] 
[ 6, 2, 4 ] - [ 6, 3, 4 ] 
[ 4, 1, 7 ] - [ 4, 8, 7 ] 

Cartan matrix

(1 0 1 1 0 0 1 0)
(1 1 0 1 0 0 1 1)
(0 0 1 1 0 0 0 1)
(1 0 1 1 0 1 1 1)
(0 1 1 1 1 1 0 1)
(0 1 1 1 0 1 0 1)
(0 0 0 1 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1542    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1326    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1295    permutation [ 6, 2, 1, 7, 4, 8, 5, 3 ]
vertex  5 -> Algebra 1339    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra 1335    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  8 -> Algebra 1523    permutation [ 1, 4, 3, 8, 5, 6, 7, 2 ]

Algebra 1331

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 5, 3 ], [ 6, 4 ], [ 7, 6 ], [ 8, 6 ]

Relations

[ 3, 4, 1 ] 
[ 6, 4, 1 ] 
[ 4, 5, 2 ] 
[ 8, 6, 4 ] 
[ 2, 4, 5 ] 
[ 3, 4, 5 ] 
[ 6, 4, 8 ] 
[ 4, 1, 3 ] - [ 4, 5, 3 ] 
[ 1, 3, 4 ] - [ 1, 6, 4 ] 
[ 5, 2, 4 ] - [ 5, 3, 4 ] 
[ 4, 1, 6 ] - [ 4, 8, 6 ] 

Cartan matrix

(1 0 1 1 0 1 0 0)
(1 1 0 1 0 1 0 1)
(0 0 1 1 0 0 0 1)
(1 0 1 1 1 1 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1415    permutation [ 3, 4, 8, 7, 6, 5, 2, 1 ]
vertex  2 -> Algebra 1320    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1479    permutation [ 1, 6, 2, 8, 3, 5, 7, 4 ]
vertex  6 -> Algebra 1482    permutation [ 1, 3, 2, 8, 4, 5, 7, 6 ]
vertex  7 -> Algebra  836    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1468    permutation [ 3, 4, 8, 1, 7, 6, 2, 5 ]

Algebra 1332

Quiver

[ 1, 2 ], [ 1, 4 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 1 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 2, 8, 1 ] 
[ 8, 1, 2 ] 
[ 4, 5, 3 ] 
[ 1, 4, 5 ] 
[ 3, 4, 5 ] 
[ 4, 8, 6 ] 
[ 6, 4, 8 ] 
[ 4, 5, 1 ] - [ 4, 8, 1 ] 
[ 5, 1, 4 ] - [ 5, 3, 4 ] 
[ 8, 1, 4 ] - [ 8, 6, 4 ] 
[ 1, 2, 8 ] - [ 1, 4, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 1)
(0 1 0 0 0 1 1 1)
(0 0 1 1 0 0 0 1)
(1 0 0 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1333    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1030    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1318    permutation [ 3, 5, 6, 8, 7, 1, 2, 4 ]
vertex  7 -> Algebra 1419    permutation [ 3, 5, 8, 7, 6, 1, 2, 4 ]

Algebra 1333

Quiver

[ 1, 4 ], [ 2, 4 ], [ 3, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 4, 5, 2 ] 
[ 1, 4, 5, 3 ] 
[ 8, 6, 1, 4 ] 
[ 2, 4, 5 ] 
[ 3, 1, 4, 5 ] 
[ 1, 4, 8, 6 ] 
[ 6, 1, 4, 8 ] 
[ 4, 5, 3, 1 ] - [ 4, 8, 6, 1 ] 
[ 5, 2, 4 ] - [ 5, 3, 1, 4 ] 

Cartan matrix

(1 0 0 1 1 0 0 1)
(0 1 0 1 0 1 1 1)
(1 0 1 1 0 0 0 1)
(1 0 1 1 1 1 1 1)
(1 1 1 1 1 0 0 1)
(1 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  836    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1322    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1332    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1312    permutation [ 3, 4, 6, 8, 7, 5, 2, 1 ]
vertex  7 -> Algebra 1415    permutation [ 3, 4, 8, 7, 6, 5, 2, 1 ]
vertex  8 -> Algebra 1225    permutation [ 3, 8, 4, 6, 7, 5, 2, 1 ]

Algebra 1334

Quiver

[ 1, 6 ], [ 2, 4 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 4, 8 ], [ 5, 2 ], [ 6, 4 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 6, 4, 3, 1 ] 
[ 4, 3, 5, 2 ] 
[ 1, 6, 4, 3 ] 
[ 5, 2, 4, 3 ] 
[ 8, 6, 4 ] 
[ 2, 4, 3, 5 ] 
[ 6, 4, 8 ] 
[ 3, 1, 6, 4 ] - [ 3, 5, 2, 4 ] 
[ 4, 3, 1, 6 ] - [ 4, 8, 6 ] 

Cartan matrix

(1 0 0 1 0 1 1 0)
(1 1 1 1 0 1 1 1)
(1 1 1 1 1 1 1 0)
(1 0 1 1 1 1 1 1)
(0 1 0 1 1 0 0 1)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1300    permutation [ 3, 6, 1, 7, 4, 8, 5, 2 ]
vertex  3 -> Algebra  836    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  936    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  6 -> Algebra 1296    permutation [ 3, 2, 1, 7, 6, 8, 5, 4 ]
vertex  7 -> Algebra 1479    permutation [ 1, 6, 2, 8, 3, 5, 7, 4 ]
vertex  8 -> Algebra 1504    permutation [ 1, 4, 3, 8, 5, 6, 7, 2 ]

Algebra 1335

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 2 ], [ 5, 3 ], [ 6, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 7 ]

Relations

[ 3, 4, 6, 1 ] 
[ 7, 6, 1 ] 
[ 4, 5, 2 ] 
[ 6, 1, 3, 4 ] 
[ 2, 4, 5 ] 
[ 3, 4, 5 ] 
[ 8, 7, 6 ] 
[ 7, 6, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 1, 3 ] 
[ 5, 2, 4 ] - [ 5, 3, 4 ] 
[ 1, 3, 4, 6 ] - [ 1, 7, 6 ] 
[ 6, 1, 7 ] - [ 6, 8, 7 ] 

Cartan matrix

(1 0 1 1 0 1 1 0)
(1 1 0 1 0 1 1 1)
(0 0 1 1 0 1 0 1)
(1 0 1 1 1 1 1 1)
(0 1 1 1 1 1 0 1)
(1 0 1 0 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1525    permutation [ 4, 5, 6, 8, 7, 1, 2, 3 ]
vertex  2 -> Algebra 1323    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1296    permutation [ 3, 2, 1, 7, 6, 8, 5, 4 ]
vertex  4 -> Algebra 1329    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra 1353    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  836    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1522    permutation [ 6, 3, 5, 2, 4, 7, 8, 1 ]
vertex  8 -> Algebra 1526    permutation [ 3, 2, 1, 7, 8, 6, 5, 4 ]

Algebra 1339

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 4 ], [ 8, 7 ]

Relations

[ 3, 4, 1 ] 
[ 7, 4, 1 ] 
[ 4, 5, 2 ] 
[ 8, 7, 4 ] 
[ 2, 4, 5 ] 
[ 3, 4, 5 ] 
[ 7, 4, 8 ] 
[ 4, 1, 3 ] - [ 4, 5, 3 ] 
[ 1, 3, 4 ] - [ 1, 7, 4 ] 
[ 5, 2, 4 ] - [ 5, 3, 4 ] 
[ 4, 1, 7 ] - [ 4, 8, 7 ] 

Cartan matrix

(1 0 1 1 0 0 1 0)
(1 1 0 1 0 0 1 1)
(0 0 1 1 0 0 0 1)
(1 0 1 1 1 1 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1538    permutation [ 3, 4, 1, 8, 7, 5, 2, 6 ]
vertex  2 -> Algebra 1168    permutation [ 2, 1, 4, 3, 8, 5, 6, 7 ]
vertex  3 -> Algebra 1239    permutation [ 2, 1, 7, 4, 8, 5, 6, 3 ]
vertex  5 -> Algebra 1344    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1329    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1480    permutation [ 3, 4, 8, 6, 1, 7, 2, 5 ]

Algebra 1344

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 5 ], [ 8, 7 ]

Relations

[ 3, 4, 5, 1 ] 
[ 7, 5, 1 ] 
[ 4, 5, 1, 3 ] 
[ 6, 4, 5 ] 
[ 8, 7, 5 ] 
[ 4, 5, 6 ] 
[ 7, 5, 8 ] 
[ 5, 1, 3, 4 ] - [ 5, 6, 4 ] 
[ 1, 3, 4, 5 ] - [ 1, 7, 5 ] 
[ 5, 1, 7 ] - [ 5, 8, 7 ] 

Cartan matrix

(1 0 1 1 1 0 1 0)
(1 1 0 1 1 0 1 1)
(0 0 1 1 1 0 0 1)
(1 0 0 1 1 0 1 1)
(1 0 1 1 1 1 1 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1320    permutation [ 3, 5, 1, 8, 7, 4, 2, 6 ]
vertex  2 -> Algebra 1300    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1546    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1339    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1353    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1479    permutation [ 3, 4, 8, 6, 1, 7, 2, 5 ]

Algebra 1353

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 7 ]

Relations

[ 3, 4, 5, 6, 1 ] 
[ 7, 6, 1 ] 
[ 4, 5, 6, 1, 3 ] 
[ 5, 6, 1, 3, 4 ] 
[ 6, 1, 3, 4, 5 ] 
[ 8, 7, 6 ] 
[ 7, 6, 8 ] 
[ 1, 3, 4, 5, 6 ] - [ 1, 7, 6 ] 
[ 6, 1, 7 ] - [ 6, 8, 7 ] 

Cartan matrix

(1 0 1 1 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 0 1 1 1 1 0 1)
(1 0 0 1 1 1 1 1)
(1 0 1 0 1 1 1 1)
(1 0 1 1 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1313    permutation [ 3, 5, 1, 8, 7, 4, 2, 6 ]
vertex  2 -> Algebra 1306    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1335    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1344    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1550    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1541    permutation [ 6, 1, 5, 3, 2, 4, 8, 7 ]

Algebra 1363

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 6 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 6, 8, 1 ] 
[ 3, 4, 8, 2 ] 
[ 5, 6, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 6, 8, 2, 5 ] 
[ 1, 6, 8 ] 
[ 8, 1, 6 ] - [ 8, 2, 5, 6 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 1 1 1 1 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 1 1 0 1)
(0 0 0 0 1 1 0 1)
(0 1 1 0 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  857    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1383    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra 1236    permutation [ 4, 5, 6, 8, 7, 1, 3, 2 ]
vertex  7 -> Algebra 1443    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1441    permutation [ 5, 4, 7, 1, 2, 3, 6, 8 ]

Algebra 1365

Quiver

[ 1, 2 ], [ 1, 7 ], [ 2, 3 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 7, 6, 1 ] 
[ 3, 4, 2 ] 
[ 5, 6, 1, 2 ] 
[ 4, 2, 3 ] 
[ 6, 1, 2, 5 ] 
[ 6, 1, 7 ] 
[ 1, 2, 8 ] 
[ 4, 2, 8 ] 
[ 2, 5, 6, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 
[ 1, 2, 5, 6 ] - [ 1, 7, 6 ] 

Cartan matrix

(1 1 1 0 1 1 1 0)
(1 1 1 1 1 1 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 1 1 0 0)
(1 0 0 0 1 1 0 0)
(1 1 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1439    permutation [ 5, 8, 7, 4, 2, 3, 6, 1 ]
vertex  2 -> Algebra 1546    permutation [ 5, 8, 4, 2, 1, 3, 6, 7 ]
vertex  3 -> Algebra 1186    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1239    permutation [ 8, 5, 6, 1, 7, 4, 3, 2 ]
vertex  8 -> Algebra  857    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1366

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 6 ], [ 6, 1 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 8, 2, 5, 6, 1 ] 
[ 3, 4, 8, 2 ] 
[ 5, 6, 1, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 1, 8, 2, 5, 6 ] 
[ 7, 5, 6 ] 
[ 5, 6, 7 ] 
[ 6, 1, 8, 2, 5 ] - [ 6, 7, 5 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 6, 1, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(1 1 1 1 1 1 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 1 1 0 1)
(1 0 0 0 1 1 0 1)
(1 1 1 0 1 1 1 1)
(0 0 0 0 1 0 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1386    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1187    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1220    permutation [ 4, 5, 6, 7, 1, 8, 3, 2 ]
vertex  5 -> Algebra 1376    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1516    permutation [ 8, 5, 6, 7, 1, 4, 3, 2 ]

Algebra 1373

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 7 ], [ 6, 7 ], [ 7, 2 ], [ 8, 2 ]

Relations

[ 8, 2, 5, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 1, 8, 2, 5 ] 
[ 7, 2, 5 ] 
[ 2, 5, 7 ] 
[ 5, 1, 8, 2 ] - [ 5, 7, 2 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 1, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 1 0 0 1)
(1 1 1 0 1 0 1 1)
(0 1 1 1 0 1 1 0)
(0 1 1 1 0 0 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra 1191    permutation [ 7, 1, 8, 5, 3, 4, 6, 2 ]
vertex  3 -> Algebra 1194    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1376    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1556    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1376

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 8, 2, 5, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 1, 8, 2, 5 ] 
[ 6, 2, 5 ] 
[ 2, 5, 6 ] 
[ 5, 1, 8, 2 ] - [ 5, 6, 2 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 1, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 1 0 0 1)
(1 1 1 0 1 1 1 1)
(0 1 1 1 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra 1113    permutation [ 1, 8, 5, 3, 4, 6, 7, 2 ]
vertex  3 -> Algebra 1030    permutation [ 1, 8, 3, 2, 4, 6, 7, 5 ]
vertex  6 -> Algebra 1366    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1373    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1466    permutation [ 1, 2, 3, 8, 4, 6, 7, 5 ]

Algebra 1383

Quiver

[ 1, 6 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 8 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 8, 1 ] 
[ 5, 8, 2 ] 
[ 6, 8, 2 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 6, 8 ] 
[ 8, 2, 5 ] - [ 8, 3, 5 ] 
[ 8, 1, 6 ] - [ 8, 2, 6 ] 
[ 2, 5, 8 ] - [ 2, 6, 8 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 0 0 1 1 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 0 1 0 1)
(1 0 0 0 1 0 0 1)
(0 0 1 0 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  867    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1390    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  4 -> Algebra 1278    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1363    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1404    permutation [ 2, 4, 5, 7, 8, 3, 6, 1 ]

Algebra 1385

Quiver

[ 1, 2 ], [ 1, 3 ], [ 1, 7 ], [ 2, 6 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 3, 8, 1 ] 
[ 7, 6, 1 ] 
[ 6, 1, 2 ] 
[ 8, 1, 3 ] 
[ 2, 8, 4 ] 
[ 6, 1, 7 ] 
[ 4, 2, 8 ] 
[ 2, 6, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 1, 2, 6 ] - [ 1, 7, 6 ] 
[ 1, 2, 8 ] - [ 1, 3, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 0 0 1 1 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 0 1 0 0)
(0 0 0 0 1 0 0 0)
(1 0 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1539    permutation [ 2, 1, 4, 7, 6, 8, 5, 3 ]
vertex  4 -> Algebra 1300    permutation [ 2, 8, 4, 5, 1, 3, 6, 7 ]
vertex  5 -> Algebra 1546    permutation [ 2, 5, 4, 8, 1, 3, 6, 7 ]
vertex  8 -> Algebra  867    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1386

Quiver

[ 1, 8 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 6, 1 ] 
[ 5, 8, 2 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 8, 2, 6 ] 
[ 7, 2, 6 ] 
[ 2, 6, 7 ] 
[ 6, 1, 8, 2 ] - [ 6, 7, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 5 ] 
[ 2, 5, 8 ] - [ 2, 6, 1, 8 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(1 1 0 0 1 1 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 0 1 0 1)
(0 0 0 0 1 0 0 1)
(1 1 1 0 1 1 1 1)
(0 1 0 0 1 0 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1394    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1415    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra 1281    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1366    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  8 -> Algebra 1558    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1390

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 6 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 6, 8, 1 ] 
[ 6, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 5, 6, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 8, 3, 5 ] 
[ 1, 2, 6, 8 ] 
[ 8, 1, 2, 6 ] - [ 8, 3, 5, 6 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(0 1 1 0 0 1 0 1)
(1 0 1 1 1 1 0 1)
(1 1 0 1 0 0 0 1)
(1 0 0 0 1 1 0 1)
(1 0 1 0 0 1 0 1)
(1 1 0 0 0 1 1 0)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  870    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1283    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1383    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1444    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1561    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1392

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 8 ], [ 3, 5 ], [ 3, 8 ], [ 4, 2 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 1 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 3, 8, 1 ] 
[ 7, 2, 8, 1 ] 
[ 5, 6, 3 ] 
[ 2, 8, 4 ] 
[ 6, 3, 5 ] 
[ 2, 8, 1, 7 ] 
[ 4, 2, 8 ] 
[ 6, 3, 8 ] 
[ 8, 1, 7, 2 ] - [ 8, 4, 2 ] 
[ 8, 1, 3 ] - [ 8, 6, 3 ] 
[ 3, 5, 6 ] - [ 3, 8, 6 ] 
[ 1, 3, 8 ] - [ 1, 7, 2, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 1 0 0 1 0 1)
(0 0 1 1 1 1 0 1)
(0 1 0 1 0 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 1 0 0 0 1 1 1)
(1 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1516    permutation [ 7, 6, 3, 5, 1, 2, 4, 8 ]
vertex  4 -> Algebra 1311    permutation [ 4, 1, 6, 3, 5, 7, 2, 8 ]
vertex  6 -> Algebra 1539    permutation [ 8, 1, 4, 7, 2, 6, 5, 3 ]
vertex  8 -> Algebra  870    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1394

Quiver

[ 1, 8 ], [ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 6 ], [ 6, 7 ], [ 6, 8 ], [ 7, 5 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 1 ] 
[ 1, 8, 2 ] 
[ 6, 8, 2 ] 
[ 4, 8, 3 ] 
[ 5, 6, 8, 3 ] 
[ 8, 3, 4 ] 
[ 7, 5, 6 ] 
[ 5, 6, 7 ] 
[ 6, 7, 5 ] - [ 6, 8, 3, 5 ] 
[ 8, 2, 6 ] - [ 8, 3, 5, 6 ] 
[ 2, 1, 8 ] - [ 2, 6, 8 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 8 ] 

Cartan matrix

(1 0 1 0 1 0 0 1)
(1 1 1 0 1 1 1 1)
(0 0 1 1 1 1 0 1)
(0 1 0 1 0 0 0 1)
(0 0 0 0 1 1 0 1)
(0 0 1 0 1 1 1 1)
(0 0 0 0 1 0 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  3 -> Algebra 1419    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra 1288    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1113    permutation [ 1, 8, 2, 3, 4, 5, 7, 6 ]
vertex  6 -> Algebra 1386    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]

Algebra 1404

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 5 ], [ 3, 5 ], [ 5, 1 ], [ 5, 6 ], [ 5, 8 ], [ 6, 2 ], [ 6, 3 ], [ 7, 5 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 3, 5, 1 ] 
[ 7, 5, 1 ] 
[ 5, 6, 2 ] 
[ 8, 7, 5 ] 
[ 2, 5, 6 ] 
[ 3, 5, 6 ] 
[ 7, 5, 8 ] 
[ 5, 1, 3 ] - [ 5, 6, 3 ] 
[ 1, 3, 5 ] - [ 1, 7, 5 ] 
[ 6, 2, 5 ] - [ 6, 3, 5 ] 
[ 5, 1, 7 ] - [ 5, 8, 7 ] 

Cartan matrix

(1 0 1 0 1 0 1 0)
(1 1 0 1 1 0 1 1)
(0 0 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 0 1 1 1 1 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1444    permutation [ 7, 6, 2, 3, 1, 8, 4, 5 ]
vertex  2 -> Algebra 1245    permutation [ 1, 2, 6, 3, 7, 8, 4, 5 ]
vertex  3 -> Algebra 1443    permutation [ 3, 6, 2, 1, 7, 8, 4, 5 ]
vertex  4 -> Algebra 1383    permutation [ 8, 1, 6, 2, 3, 7, 4, 5 ]

Algebra 1414

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 7 ], [ 7, 1 ], [ 8, 2 ]

Relations

[ 8, 2, 6, 7, 1 ] 
[ 3, 5, 8, 2 ] 
[ 6, 7, 1, 8, 2 ] 
[ 5, 8, 2, 3 ] 
[ 8, 2, 3, 5 ] 
[ 7, 1, 8, 2, 6 ] 
[ 1, 8, 2, 6, 7 ] 
[ 2, 3, 5, 8 ] - [ 2, 6, 7, 1, 8 ] 

Cartan matrix

(1 1 1 0 0 1 0 1)
(1 1 1 0 1 1 1 1)
(0 0 1 0 1 0 0 1)
(0 1 0 1 1 1 1 1)
(0 1 0 0 1 1 1 1)
(1 0 0 0 0 1 1 1)
(1 1 1 0 0 0 1 1)
(0 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1565    permutation [ 2, 4, 3, 1, 5, 8, 6, 7 ]
vertex  2 -> Algebra 1418    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1201    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1322    permutation [ 8, 2, 1, 6, 7, 5, 4, 3 ]
vertex  6 -> Algebra 1415    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1320    permutation [ 8, 2, 1, 6, 7, 5, 4, 3 ]

Algebra 1415

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 7, 2 ], [ 8, 2 ]

Relations

[ 8, 2, 6, 1 ] 
[ 3, 5, 8, 2 ] 
[ 5, 8, 2, 3 ] 
[ 8, 2, 3, 5 ] 
[ 1, 8, 2, 6 ] 
[ 7, 2, 6 ] 
[ 2, 6, 7 ] 
[ 6, 1, 8, 2 ] - [ 6, 7, 2 ] 
[ 2, 3, 5, 8 ] - [ 2, 6, 1, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(1 1 1 0 1 1 0 1)
(0 0 1 0 1 0 0 1)
(0 1 0 1 1 1 0 1)
(0 1 0 0 1 1 0 1)
(1 1 1 0 0 1 1 1)
(0 1 1 0 1 0 1 0)
(0 1 1 0 0 1 0 1)

Good mutations

vertex  2 -> Algebra 1419    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1203    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1333    permutation [ 8, 7, 1, 2, 6, 5, 4, 3 ]
vertex  5 -> Algebra 1386    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra 1414    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1331    permutation [ 8, 7, 1, 2, 6, 5, 4, 3 ]

Algebra 1418

Quiver

[ 1, 8 ], [ 2, 6 ], [ 2, 7 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 8 ], [ 6, 8 ], [ 7, 1 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 7, 1 ] 
[ 6, 8, 2 ] 
[ 7, 1, 8, 2 ] 
[ 5, 8, 3 ] 
[ 6, 8, 3 ] 
[ 8, 3, 5 ] 
[ 1, 8, 2, 7 ] 
[ 8, 2, 6 ] - [ 8, 3, 6 ] 
[ 2, 6, 8 ] - [ 2, 7, 1, 8 ] 
[ 3, 5, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 1 1 0 0 1 0 1)
(1 1 0 0 0 1 1 1)
(0 0 1 0 1 1 0 1)
(0 1 0 1 1 0 1 1)
(0 1 0 0 1 0 1 1)
(0 0 0 0 0 1 0 1)
(1 0 1 0 0 0 1 1)
(0 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1556    permutation [ 6, 8, 1, 7, 3, 4, 5, 2 ]
vertex  2 -> Algebra 1194    permutation [ 6, 1, 8, 7, 3, 4, 5, 2 ]
vertex  4 -> Algebra 1020    permutation [ 6, 8, 1, 2, 7, 5, 4, 3 ]
vertex  6 -> Algebra 1414    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  8 -> Algebra 1019    permutation [ 6, 8, 1, 2, 7, 5, 4, 3 ]

Algebra 1419

Quiver

[ 1, 8 ], [ 2, 1 ], [ 2, 6 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 8 ], [ 6, 7 ], [ 6, 8 ], [ 7, 3 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 8, 2, 1 ] 
[ 1, 8, 2 ] 
[ 6, 8, 2 ] 
[ 5, 8, 3 ] 
[ 8, 3, 5 ] 
[ 7, 3, 6 ] 
[ 3, 6, 7 ] 
[ 6, 7, 3 ] - [ 6, 8, 3 ] 
[ 8, 2, 6 ] - [ 8, 3, 6 ] 
[ 2, 1, 8 ] - [ 2, 6, 8 ] 
[ 3, 5, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(1 1 1 0 0 1 1 1)
(0 0 1 0 1 1 0 1)
(0 1 0 1 1 0 0 1)
(0 1 0 0 1 0 0 1)
(0 0 1 0 0 1 1 1)
(0 0 1 0 1 0 1 0)
(0 1 1 0 0 1 0 1)

Good mutations

vertex  4 -> Algebra 1332    permutation [ 6, 7, 1, 8, 2, 5, 4, 3 ]
vertex  5 -> Algebra 1394    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra 1415    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1194    permutation [ 7, 1, 8, 2, 3, 4, 5, 6 ]

Algebra 1423

Quiver

[ 1, 7 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 5, 1 ], [ 5, 6 ], [ 5, 8 ], [ 6, 2 ], [ 7, 5 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 7, 5, 1 ] 
[ 3, 8, 2 ] 
[ 8, 2, 3 ] 
[ 1, 7, 5 ] 
[ 6, 2, 5 ] 
[ 2, 5, 6 ] 
[ 7, 5, 8 ] 
[ 5, 6, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 7, 5 ] 
[ 5, 1, 7 ] - [ 5, 8, 7 ] 
[ 2, 3, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 0 0 1 0)
(1 1 1 1 1 0 1 1)
(0 0 1 1 0 0 1 1)
(0 0 0 1 0 0 0 0)
(1 1 0 0 1 1 1 1)
(0 1 1 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 0 0 1 0 1 1)

Good mutations

vertex  4 -> Algebra 1441    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1443    permutation [ 5, 6, 2, 1, 7, 3, 4, 8 ]

Algebra 1439

Quiver

[ 1, 7 ], [ 2, 3 ], [ 2, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 5 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 7, 5, 1 ] 
[ 3, 8, 2 ] 
[ 4, 5, 8, 2 ] 
[ 8, 2, 3 ] 
[ 1, 7, 5 ] 
[ 6, 4, 5 ] 
[ 4, 5, 6 ] 
[ 7, 5, 8 ] 
[ 5, 6, 4 ] - [ 5, 8, 2, 4 ] 
[ 8, 2, 4, 5 ] - [ 8, 7, 5 ] 
[ 5, 1, 7 ] - [ 5, 8, 7 ] 
[ 2, 3, 8 ] - [ 2, 4, 5, 8 ] 

Cartan matrix

(1 0 0 0 0 0 1 0)
(1 1 1 1 1 0 1 1)
(0 0 1 0 0 0 1 1)
(1 0 0 1 1 0 1 1)
(1 1 0 1 1 1 1 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 0 1 1 0 1 1)

Good mutations

vertex  2 -> Algebra 1441    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1238    permutation [ 8, 1, 7, 2, 3, 4, 6, 5 ]
vertex  6 -> Algebra 1273    permutation [ 6, 8, 1, 7, 2, 3, 4, 5 ]
vertex  8 -> Algebra 1365    permutation [ 8, 5, 6, 4, 1, 7, 3, 2 ]

Algebra 1441

Quiver

[ 1, 7 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 5, 8 ], [ 6, 2 ], [ 7, 5 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 7, 5, 1 ] 
[ 4, 8, 2 ] 
[ 8, 2, 4 ] 
[ 1, 7, 5 ] 
[ 6, 2, 5 ] 
[ 2, 5, 6 ] 
[ 7, 5, 8 ] 
[ 5, 6, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 7, 5 ] 
[ 5, 1, 7 ] - [ 5, 8, 7 ] 
[ 2, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 0 0 1 0)
(1 1 0 1 1 0 1 1)
(0 0 1 1 0 0 1 1)
(0 0 0 1 0 0 1 1)
(1 1 0 0 1 1 1 1)
(0 1 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 0 0 1 0 1 1)

Good mutations

vertex  3 -> Algebra 1423    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1439    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1363    permutation [ 4, 5, 6, 2, 1, 7, 3, 8 ]

Algebra 1443

Quiver

[ 1, 2 ], [ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 5 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 2, 3, 8, 1 ] 
[ 4, 5, 8, 1 ] 
[ 3, 8, 1, 2 ] 
[ 8, 1, 2, 3 ] 
[ 5, 8, 1, 4 ] 
[ 5, 8, 6 ] 
[ 6, 5, 8 ] 
[ 8, 1, 4, 5 ] - [ 8, 6, 5 ] 
[ 1, 2, 3, 8 ] - [ 1, 4, 5, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(0 1 1 0 0 1 1 1)
(1 0 1 1 1 1 1 1)
(0 0 0 1 1 0 0 1)
(1 1 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1404    permutation [ 4, 3, 1, 7, 8, 2, 5, 6 ]
vertex  3 -> Algebra 1242    permutation [ 3, 4, 5, 8, 6, 7, 2, 1 ]
vertex  7 -> Algebra 1363    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1423    permutation [ 4, 3, 6, 7, 1, 2, 5, 8 ]

Algebra 1444

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 5, 8, 6, 1 ] 
[ 3, 8, 2 ] 
[ 4, 5, 8, 2 ] 
[ 8, 2, 3 ] 
[ 5, 8, 2, 4 ] 
[ 1, 5, 8, 6 ] 
[ 6, 1, 5, 8 ] 
[ 8, 2, 4, 5 ] - [ 8, 6, 1, 5 ] 
[ 2, 3, 8 ] - [ 2, 4, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 1)
(0 1 1 1 1 1 1 1)
(1 0 1 0 0 1 1 1)
(0 0 0 1 1 1 1 1)
(0 1 0 0 1 1 1 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  3 -> Algebra 1246    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1404    permutation [ 5, 3, 4, 7, 8, 2, 1, 6 ]
vertex  7 -> Algebra 1390    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1558    permutation [ 8, 5, 3, 1, 7, 2, 4, 6 ]

Algebra 1463

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 1 ], [ 6, 3 ], [ 7, 2 ], [ 8, 1 ], [ 8, 7 ]

Relations

[ 2, 6, 3 ] 
[ 5, 3, 4 ] 
[ 6, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 2, 6 ] 
[ 2, 8, 7 ] 
[ 1, 2, 8 ] 
[ 7, 2, 8 ] 
[ 2, 6, 1 ] - [ 2, 8, 1 ] 
[ 6, 1, 2 ] - [ 6, 3, 2 ] 
[ 8, 1, 2 ] - [ 8, 7, 2 ] 
[ 4, 5, 3 ] - [ 4, 6, 3 ] 
[ 3, 2, 6 ] - [ 3, 4, 6 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(1 1 0 0 0 1 0 1)
(1 1 1 1 0 1 0 1)
(1 1 1 1 1 1 0 0)
(0 1 1 0 1 0 0 1)
(1 1 1 0 0 1 0 0)
(0 1 0 0 0 1 1 0)
(1 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1526    permutation [ 6, 5, 1, 8, 7, 2, 4, 3 ]
vertex  2 -> Algebra 1017    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1571    permutation [ 6, 1, 3, 7, 2, 8, 5, 4 ]
vertex  4 -> Algebra 1468    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra 1316    permutation [ 3, 4, 2, 8, 7, 1, 5, 6 ]
vertex  6 -> Algebra 1315    permutation [ 3, 4, 2, 8, 7, 1, 5, 6 ]
vertex  7 -> Algebra 1525    permutation [ 3, 4, 2, 7, 8, 1, 5, 6 ]

Algebra 1464

Quiver

[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 8, 2, 3 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 3, 4, 6 ] 
[ 7, 4, 6 ] 
[ 4, 6, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 6, 2 ] - [ 3, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 6, 2, 3 ] 
[ 6, 2, 3, 4 ] - [ 6, 7, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 0 0 0)
(1 1 1 1 0 1 0 1)
(1 1 1 1 1 1 0 0)
(0 0 1 0 1 0 0 1)
(1 1 1 1 0 1 1 0)
(0 0 0 1 1 0 1 0)
(1 1 0 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1319    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1019    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1257    permutation [ 7, 2, 1, 3, 8, 4, 5, 6 ]
vertex  8 -> Algebra 1018    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1466

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 2, 8 ], [ 3, 5 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 2 ], [ 6, 7 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 3, 5, 2 ] 
[ 5, 2, 3 ] 
[ 1, 2, 4 ] 
[ 5, 2, 4 ] 
[ 2, 8, 6 ] 
[ 1, 2, 8 ] 
[ 6, 2, 8 ] 
[ 2, 4, 1 ] - [ 2, 8, 1 ] 
[ 4, 1, 2 ] - [ 4, 5, 2 ] 
[ 8, 1, 2 ] - [ 8, 6, 2 ] 
[ 2, 3, 5 ] - [ 2, 4, 5 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(1 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 1)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1539    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1020    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1376    permutation [ 1, 2, 3, 5, 8, 6, 7, 4 ]
vertex  6 -> Algebra 1516    permutation [ 4, 6, 8, 7, 1, 5, 3, 2 ]
vertex  7 -> Algebra 1556    permutation [ 1, 2, 3, 5, 8, 7, 6, 4 ]

Algebra 1468

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 1 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 1 ], [ 8, 7 ]

Relations

[ 2, 4, 6, 3 ] 
[ 1, 2, 4 ] 
[ 6, 3, 2, 4 ] 
[ 3, 2, 4, 6 ] 
[ 2, 8, 7 ] 
[ 1, 2, 8 ] 
[ 7, 2, 8 ] 
[ 2, 4, 1 ] - [ 2, 8, 1 ] 
[ 4, 1, 2 ] - [ 4, 6, 3, 2 ] 
[ 8, 1, 2 ] - [ 8, 7, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(1 1 0 1 0 1 0 1)
(1 1 1 1 0 0 0 1)
(1 1 1 1 0 1 0 0)
(0 1 1 0 1 1 0 1)
(0 1 1 0 0 1 0 1)
(0 1 0 1 0 1 1 0)
(1 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1541    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1023    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1331    permutation [ 4, 7, 1, 2, 8, 6, 5, 3 ]
vertex  4 -> Algebra 1203    permutation [ 1, 3, 2, 5, 6, 8, 7, 4 ]
vertex  5 -> Algebra 1258    permutation [ 4, 2, 1, 3, 8, 6, 5, 7 ]
vertex  6 -> Algebra 1463    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1313    permutation [ 4, 3, 1, 7, 8, 6, 5, 2 ]

Algebra 1479

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 8, 5, 1 ] 
[ 8, 5, 6, 3 ] 
[ 2, 8, 4 ] 
[ 1, 2, 8, 5 ] 
[ 6, 3, 8, 5 ] 
[ 3, 8, 5, 6 ] 
[ 4, 2, 8 ] 
[ 8, 4, 2 ] - [ 8, 5, 1, 2 ] 
[ 5, 1, 2, 8 ] - [ 5, 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 0 1 1 0 1)
(1 1 1 1 1 0 0 1)
(0 1 0 1 0 0 0 0)
(1 1 1 0 1 1 0 1)
(0 0 1 1 0 1 0 1)
(0 1 0 0 1 1 1 1)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1480    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1344    permutation [ 5, 7, 1, 2, 8, 4, 6, 3 ]
vertex  4 -> Algebra 1541    permutation [ 8, 5, 4, 1, 7, 2, 3, 6 ]
vertex  5 -> Algebra 1331    permutation [ 1, 3, 5, 8, 6, 2, 7, 4 ]
vertex  7 -> Algebra 1334    permutation [ 1, 3, 5, 8, 6, 2, 7, 4 ]
vertex  8 -> Algebra 1054    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1480

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 5, 1 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 1 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 2, 5, 6, 3 ] 
[ 1, 2, 5 ] 
[ 6, 3, 2, 5 ] 
[ 3, 2, 5, 6 ] 
[ 2, 8, 7 ] 
[ 1, 2, 8 ] 
[ 7, 2, 8 ] 
[ 2, 5, 1 ] - [ 2, 8, 1 ] 
[ 5, 1, 2 ] - [ 5, 6, 3, 2 ] 
[ 8, 1, 2 ] - [ 8, 7, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(1 1 0 1 1 1 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 1 1 0 1 1 0 0)
(0 1 1 1 0 1 0 1)
(0 1 0 0 1 1 1 0)
(1 1 0 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1246    permutation [ 7, 5, 6, 3, 2, 8, 4, 1 ]
vertex  2 -> Algebra 1055    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1339    permutation [ 5, 7, 1, 2, 8, 4, 6, 3 ]
vertex  4 -> Algebra 1523    permutation [ 5, 2, 1, 3, 4, 8, 6, 7 ]
vertex  5 -> Algebra 1482    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1248    permutation [ 7, 5, 6, 3, 2, 8, 4, 1 ]
vertex  8 -> Algebra 1479    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1482

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 5, 6 ], [ 5, 8 ], [ 6, 2 ], [ 6, 3 ], [ 7, 5 ], [ 8, 1 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 2, 5, 8, 1 ] 
[ 5, 6, 3 ] 
[ 2, 5, 6 ] 
[ 3, 5, 6 ] 
[ 5, 8, 7 ] 
[ 1, 2, 5, 8 ] 
[ 7, 5, 8 ] 
[ 5, 6, 2 ] - [ 5, 8, 1, 2 ] 
[ 6, 2, 5 ] - [ 6, 3, 5 ] 
[ 8, 1, 2, 5 ] - [ 8, 7, 5 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 0 1 1 0 0 1)
(1 0 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 1 0 1 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 1 1 0)
(1 1 0 1 1 0 1 1)

Good mutations

vertex  1 -> Algebra 1558    permutation [ 2, 5, 1, 7, 4, 6, 3, 8 ]
vertex  2 -> Algebra 1480    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1538    permutation [ 1, 5, 2, 3, 6, 8, 7, 4 ]
vertex  4 -> Algebra 1571    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1522    permutation [ 7, 2, 6, 3, 5, 8, 4, 1 ]
vertex  8 -> Algebra 1331    permutation [ 1, 3, 2, 5, 6, 8, 7, 4 ]

Algebra 1490

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 5, 6 ], [ 5, 8 ], [ 6, 2 ], [ 7, 5 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 8, 2, 3 ] 
[ 6, 2, 5 ] 
[ 2, 5, 6 ] 
[ 5, 8, 7 ] 
[ 7, 5, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 2 ] 
[ 5, 6, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 7, 5 ] 
[ 2, 3, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 1 1 1 0 0 1)
(1 1 1 1 1 0 1 1)
(0 0 0 1 0 0 0 0)
(0 1 0 0 1 1 0 1)
(0 1 1 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 0 0 1 0 1 1)

Good mutations

vertex  3 -> Algebra 1319    permutation [ 1, 3, 2, 5, 6, 8, 7, 4 ]
vertex  4 -> Algebra 1494    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1225    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1538    permutation [ 1, 8, 2, 5, 6, 3, 7, 4 ]

Algebra 1494

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 6 ], [ 5, 8 ], [ 6, 2 ], [ 7, 5 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 2, 4, 1 ] 
[ 1, 2, 4 ] 
[ 8, 2, 4 ] 
[ 6, 2, 5 ] 
[ 2, 5, 6 ] 
[ 5, 8, 7 ] 
[ 7, 5, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 5, 6, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 7, 5 ] 
[ 2, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 0 1 1 0 0 1)
(1 1 1 1 1 0 1 1)
(1 1 0 1 1 0 1 1)
(0 1 0 0 1 1 0 1)
(0 1 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 0 0 1 0 1 1)

Good mutations

vertex  3 -> Algebra 1490    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1318    permutation [ 1, 3, 2, 5, 6, 8, 7, 4 ]
vertex  7 -> Algebra 1203    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1542    permutation [ 2, 7, 1, 8, 3, 4, 6, 5 ]

Algebra 1504

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 2 ], [ 5, 8 ], [ 6, 4 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 4, 2, 3, 1 ] 
[ 1, 6, 4, 2, 3 ] 
[ 5, 8, 2, 3 ] 
[ 2, 3, 1, 6, 4 ] 
[ 8, 2, 3, 5 ] 
[ 4, 2, 3, 1, 6 ] 
[ 2, 3, 5, 8 ] 
[ 3, 1, 6, 4, 2 ] - [ 3, 5, 8, 2 ] 

Cartan matrix

(1 1 0 1 0 1 1 0)
(1 1 1 0 1 1 1 0)
(1 1 1 1 1 1 1 1)
(1 1 1 1 1 0 0 0)
(0 1 0 0 1 0 0 1)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1538    permutation [ 4, 3, 2, 5, 8, 6, 1, 7 ]
vertex  2 -> Algebra 1168    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1258    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1334    permutation [ 1, 8, 3, 2, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1522    permutation [ 1, 2, 8, 5, 3, 6, 7, 4 ]
vertex  6 -> Algebra 1323    permutation [ 4, 3, 2, 5, 8, 1, 6, 7 ]
vertex  7 -> Algebra 1541    permutation [ 2, 3, 4, 1, 7, 6, 8, 5 ]
vertex  8 -> Algebra 1306    permutation [ 3, 6, 1, 7, 4, 2, 5, 8 ]

Algebra 1516

Quiver

[ 1, 5 ], [ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 8 ], [ 6, 8 ], [ 7, 6 ], [ 8, 1 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 5, 8, 1 ] 
[ 6, 8, 1 ] 
[ 4, 2, 3 ] 
[ 5, 8, 2, 3 ] 
[ 2, 3, 4 ] 
[ 6, 8, 7 ] 
[ 2, 3, 5, 8 ] 
[ 7, 6, 8 ] 
[ 3, 4, 2 ] - [ 3, 5, 8, 2 ] 
[ 8, 1, 5 ] - [ 8, 2, 3, 5 ] 
[ 8, 1, 6 ] - [ 8, 7, 6 ] 
[ 1, 5, 8 ] - [ 1, 6, 8 ] 

Cartan matrix

(1 1 0 0 1 1 0 1)
(0 1 1 0 1 0 0 0)
(0 1 1 1 1 0 1 1)
(0 1 0 1 0 0 0 0)
(0 1 0 0 1 0 1 1)
(0 1 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1366    permutation [ 5, 8, 7, 6, 2, 3, 4, 1 ]
vertex  2 -> Algebra 1466    permutation [ 5, 8, 7, 1, 6, 2, 4, 3 ]
vertex  5 -> Algebra 1392    permutation [ 5, 6, 3, 7, 4, 2, 1, 8 ]
vertex  7 -> Algebra 1315    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1561    permutation [ 8, 6, 3, 7, 4, 2, 1, 5 ]

Algebra 1522

Quiver

[ 1, 6 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 3 ], [ 6, 7 ], [ 6, 8 ], [ 8, 2 ]

Relations

[ 6, 8, 2, 5, 1 ] 
[ 2, 5, 3 ] 
[ 4, 5, 3 ] 
[ 5, 3, 4 ] 
[ 1, 6, 8, 2, 5 ] 
[ 8, 2, 5, 1, 6 ] 
[ 2, 5, 1, 6, 8 ] 
[ 5, 1, 6, 8, 2 ] - [ 5, 3, 2 ] 
[ 3, 2, 5 ] - [ 3, 4, 5 ] 

Cartan matrix

(1 1 0 0 0 1 1 1)
(1 1 0 0 1 1 1 0)
(1 1 1 1 1 1 1 0)
(1 0 0 1 1 1 1 1)
(1 1 1 0 1 1 1 1)
(0 1 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1482    permutation [ 8, 2, 4, 7, 5, 3, 1, 6 ]
vertex  2 -> Algebra 1248    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1550    permutation [ 8, 4, 2, 3, 5, 1, 6, 7 ]
vertex  4 -> Algebra 1504    permutation [ 1, 2, 5, 8, 4, 6, 7, 3 ]
vertex  6 -> Algebra 1335    permutation [ 8, 4, 2, 5, 3, 1, 6, 7 ]
vertex  7 -> Algebra 1540    permutation [ 2, 4, 8, 1, 7, 6, 3, 5 ]

Algebra 1523

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 1 ], [ 2, 6 ], [ 3, 2 ], [ 4, 2 ], [ 5, 6 ], [ 6, 3 ], [ 6, 8 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 3, 2, 1 ] 
[ 7, 4, 2, 1 ] 
[ 2, 1, 7, 4 ] 
[ 3, 2, 6 ] 
[ 8, 2, 6 ] 
[ 4, 2, 1, 7 ] 
[ 2, 6, 8 ] 
[ 1, 3, 2 ] - [ 1, 7, 4, 2 ] 
[ 6, 3, 2 ] - [ 6, 8, 2 ] 
[ 2, 1, 3 ] - [ 2, 6, 3 ] 

Cartan matrix

(1 1 1 1 0 0 1 0)
(1 1 1 0 0 1 1 0)
(0 1 1 0 0 0 0 0)
(1 1 1 1 0 1 0 0)
(0 1 1 0 1 1 0 1)
(0 1 1 0 0 1 0 1)
(0 1 0 1 0 1 1 0)
(1 1 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1571    permutation [ 3, 1, 6, 4, 2, 7, 8, 5 ]
vertex  2 -> Algebra 1261    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1283    permutation [ 6, 8, 1, 7, 4, 2, 5, 3 ]
vertex  4 -> Algebra 1329    permutation [ 1, 8, 3, 2, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1480    permutation [ 3, 2, 4, 5, 1, 7, 8, 6 ]
vertex  6 -> Algebra 1526    permutation [ 3, 8, 1, 7, 4, 2, 5, 6 ]
vertex  8 -> Algebra 1325    permutation [ 1, 4, 3, 8, 5, 6, 7, 2 ]

Algebra 1524

Quiver

[ 1, 6 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 2, 8, 3, 4, 1 ] 
[ 8, 3, 4, 1, 6, 2 ] 
[ 4, 1, 6, 2, 8, 3 ] 
[ 1, 6, 2, 8, 3, 4 ] 
[ 2, 8, 3, 4, 1, 6 ] 
[ 3, 4, 1, 6, 2, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 1 1 1 0 0 1)
(1 1 1 1 1 1 1 0)
(1 1 0 1 0 1 1 1)
(0 0 0 0 1 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 1 1 1 1 1 1)

Good mutations

vertex  3 -> Algebra 1306    permutation [ 4, 6, 1, 7, 2, 8, 3, 5 ]
vertex  5 -> Algebra 1550    permutation [ 2, 5, 8, 3, 4, 1, 6, 7 ]
vertex  6 -> Algebra 1306    permutation [ 2, 3, 8, 5, 4, 1, 6, 7 ]
vertex  7 -> Algebra 1550    permutation [ 4, 7, 1, 6, 2, 8, 3, 5 ]

Algebra 1525

Quiver

[ 1, 2 ], [ 1, 3 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 3, 8, 1 ] 
[ 7, 1, 2 ] 
[ 8, 1, 2 ] 
[ 4, 5, 6, 3 ] 
[ 5, 6, 3, 4 ] 
[ 6, 3, 4, 5 ] 
[ 1, 2, 7 ] 
[ 6, 3, 8 ] 
[ 2, 7, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 6, 3 ] 
[ 3, 4, 5, 6 ] - [ 3, 8, 6 ] 
[ 1, 2, 8 ] - [ 1, 3, 8 ] 

Cartan matrix

(1 1 1 1 1 1 0 1)
(1 1 1 1 0 1 1 1)
(0 0 1 1 1 1 0 1)
(0 0 0 1 1 1 0 0)
(0 0 1 0 1 1 0 0)
(0 0 1 1 0 1 0 0)
(1 0 1 1 1 0 1 0)
(1 0 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1542    permutation [ 6, 7, 8, 3, 2, 1, 5, 4 ]
vertex  2 -> Algebra 1313    permutation [ 8, 1, 6, 4, 5, 2, 7, 3 ]
vertex  3 -> Algebra 1312    permutation [ 8, 1, 6, 4, 5, 2, 7, 3 ]
vertex  4 -> Algebra 1463    permutation [ 6, 3, 1, 2, 7, 8, 4, 5 ]
vertex  6 -> Algebra 1335    permutation [ 6, 7, 8, 1, 2, 3, 5, 4 ]
vertex  7 -> Algebra 1285    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1526

Quiver

[ 1, 8 ], [ 2, 8 ], [ 3, 1 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ], [ 7, 2 ], [ 8, 6 ], [ 8, 7 ]

Relations

[ 8, 7, 2 ] 
[ 1, 8, 6, 3 ] 
[ 4, 5, 6, 3 ] 
[ 5, 6, 3, 4 ] 
[ 6, 3, 4, 5 ] 
[ 1, 8, 7 ] 
[ 2, 8, 7 ] 
[ 6, 3, 1, 8 ] 
[ 8, 6, 3, 1 ] - [ 8, 7, 1 ] 
[ 3, 1, 8, 6 ] - [ 3, 4, 5, 6 ] 
[ 7, 1, 8 ] - [ 7, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 1)
(0 1 1 1 0 1 0 1)
(1 0 1 1 1 1 0 1)
(0 0 0 1 1 1 0 0)
(1 0 1 0 1 1 0 0)
(1 0 1 1 0 1 0 0)
(1 1 0 0 0 1 1 1)
(1 0 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1285    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1527    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1463    permutation [ 3, 6, 8, 7, 2, 1, 5, 4 ]
vertex  4 -> Algebra 1537    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1335    permutation [ 3, 2, 1, 8, 7, 6, 4, 5 ]
vertex  6 -> Algebra 1317    permutation [ 6, 3, 8, 7, 2, 1, 5, 4 ]
vertex  7 -> Algebra 1541    permutation [ 6, 3, 8, 1, 2, 7, 5, 4 ]
vertex  8 -> Algebra 1523    permutation [ 3, 6, 1, 5, 7, 8, 4, 2 ]

Algebra 1527

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 1 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ], [ 8, 7 ]

Relations

[ 6, 3, 1, 2 ] 
[ 8, 7, 1, 2 ] 
[ 1, 2, 6, 3 ] 
[ 4, 5, 6, 3 ] 
[ 5, 6, 3, 4 ] 
[ 6, 3, 4, 5 ] 
[ 1, 2, 8, 7 ] 
[ 7, 1, 2, 8 ] 
[ 2, 6, 3, 1 ] - [ 2, 8, 7, 1 ] 
[ 3, 1, 2, 6 ] - [ 3, 4, 5, 6 ] 

Cartan matrix

(1 1 0 0 0 1 0 1)
(1 1 1 1 0 1 1 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 1 1 0 0)
(1 0 1 0 1 1 0 0)
(1 0 1 1 0 1 0 0)
(1 1 0 0 0 1 1 0)
(1 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1286    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1316    permutation [ 3, 5, 1, 8, 7, 2, 4, 6 ]
vertex  3 -> Algebra 1316    permutation [ 2, 7, 6, 4, 5, 3, 8, 1 ]
vertex  4 -> Algebra 1526    permutation [ 6, 4, 2, 8, 7, 1, 5, 3 ]
vertex  5 -> Algebra 1323    permutation [ 3, 2, 1, 8, 7, 6, 4, 5 ]
vertex  6 -> Algebra 1286    permutation [ 6, 3, 2, 8, 7, 1, 5, 4 ]
vertex  7 -> Algebra 1323    permutation [ 2, 3, 6, 4, 5, 1, 8, 7 ]
vertex  8 -> Algebra 1526    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1537

Quiver

[ 1, 8 ], [ 2, 8 ], [ 3, 1 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 3 ], [ 7, 1 ], [ 7, 2 ], [ 8, 6 ], [ 8, 7 ]

Relations

[ 8, 7, 2 ] 
[ 1, 8, 6, 3 ] 
[ 5, 3, 4 ] 
[ 6, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 8, 7 ] 
[ 2, 8, 7 ] 
[ 6, 3, 1, 8 ] 
[ 8, 6, 3, 1 ] - [ 8, 7, 1 ] 
[ 4, 5, 3 ] - [ 4, 6, 3 ] 
[ 3, 1, 8, 6 ] - [ 3, 4, 6 ] 
[ 7, 1, 8 ] - [ 7, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 1)
(0 1 1 0 0 1 0 1)
(1 0 1 1 0 1 0 1)
(1 0 1 1 1 1 0 0)
(1 0 1 0 1 0 0 1)
(1 0 1 0 0 1 0 0)
(1 1 0 0 0 1 1 1)
(1 0 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1316    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1526    permutation [ 6, 5, 8, 2, 7, 1, 4, 3 ]
vertex  4 -> Algebra 1540    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra 1526    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1316    permutation [ 6, 5, 8, 7, 2, 1, 4, 3 ]
vertex  7 -> Algebra 1540    permutation [ 6, 5, 8, 1, 2, 7, 4, 3 ]

Algebra 1538

Quiver

[ 1, 3 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 6, 8 ], [ 7, 2 ]

Relations

[ 3, 2, 6, 1 ] 
[ 4, 5, 3, 2 ] 
[ 5, 3, 2, 4 ] 
[ 3, 2, 4, 5 ] 
[ 1, 3, 2, 6 ] 
[ 7, 2, 6 ] 
[ 2, 6, 7 ] 
[ 6, 1, 3, 2 ] - [ 6, 7, 2 ] 
[ 2, 4, 5, 3 ] - [ 2, 6, 1, 3 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 1 1 1 0 1 0 1)
(0 0 1 1 1 0 0 0)
(0 1 1 0 1 1 0 1)
(1 1 1 1 0 1 1 1)
(0 1 0 1 1 0 1 0)
(0 0 0 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1490    permutation [ 1, 3, 6, 8, 4, 5, 7, 2 ]
vertex  3 -> Algebra 1339    permutation [ 3, 7, 1, 2, 6, 8, 5, 4 ]
vertex  4 -> Algebra 1482    permutation [ 1, 3, 4, 8, 2, 5, 7, 6 ]
vertex  6 -> Algebra 1320    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1504    permutation [ 7, 3, 2, 1, 4, 6, 8, 5 ]
vertex  8 -> Algebra 1542    permutation [ 3, 7, 1, 2, 8, 6, 5, 4 ]

Algebra 1539

Quiver

[ 1, 2 ], [ 1, 3 ], [ 2, 4 ], [ 2, 8 ], [ 3, 5 ], [ 4, 5 ], [ 5, 1 ], [ 6, 1 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 3, 5, 1 ] 
[ 4, 5, 1, 2 ] 
[ 8, 6, 1, 2 ] 
[ 5, 1, 3 ] 
[ 5, 1, 2, 4 ] 
[ 1, 2, 8, 6 ] 
[ 6, 1, 2, 8 ] 
[ 2, 4, 5, 1 ] - [ 2, 8, 6, 1 ] 
[ 1, 2, 4, 5 ] - [ 1, 3, 5 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(1 1 0 1 1 1 1 1)
(0 0 1 0 1 0 0 0)
(1 0 0 1 1 0 0 0)
(1 1 0 0 1 0 0 1)
(1 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1385    permutation [ 2, 1, 8, 3, 7, 5, 4, 6 ]
vertex  2 -> Algebra 1466    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1322    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1392    permutation [ 2, 5, 8, 3, 7, 6, 4, 1 ]
vertex  7 -> Algebra 1565    permutation [ 2, 7, 8, 3, 6, 1, 4, 5 ]

Algebra 1540

Quiver

[ 1, 8 ], [ 2, 8 ], [ 3, 1 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ], [ 7, 2 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 8, 7, 2 ] 
[ 1, 8, 4, 6, 3 ] 
[ 6, 3, 1, 8, 4 ] 
[ 3, 1, 8, 4, 6 ] 
[ 1, 8, 7 ] 
[ 2, 8, 7 ] 
[ 4, 6, 3, 1, 8 ] 
[ 8, 4, 6, 3, 1 ] - [ 8, 7, 1 ] 
[ 7, 1, 8 ] - [ 7, 2, 8 ] 

Cartan matrix

(1 0 0 1 0 1 0 1)
(0 1 1 1 0 1 0 1)
(1 0 1 1 0 0 0 1)
(1 0 1 1 0 1 0 0)
(1 0 1 0 1 1 0 1)
(1 0 1 0 0 1 0 1)
(1 1 0 1 0 1 1 1)
(1 0 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1325    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1541    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  4 -> Algebra 1571    permutation [ 3, 1, 6, 2, 8, 7, 4, 5 ]
vertex  5 -> Algebra 1522    permutation [ 4, 1, 7, 2, 8, 6, 5, 3 ]
vertex  6 -> Algebra 1537    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1573    permutation [ 2, 3, 1, 5, 6, 7, 8, 4 ]

Algebra 1541

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 1 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ], [ 8, 7 ]

Relations

[ 4, 6, 3, 1, 2 ] 
[ 8, 7, 1, 2 ] 
[ 1, 2, 4, 6, 3 ] 
[ 6, 3, 1, 2, 4 ] 
[ 3, 1, 2, 4, 6 ] 
[ 1, 2, 8, 7 ] 
[ 7, 1, 2, 8 ] 
[ 2, 4, 6, 3, 1 ] - [ 2, 8, 7, 1 ] 

Cartan matrix

(1 1 0 1 0 1 0 1)
(1 1 1 1 0 1 1 1)
(1 1 1 1 0 0 0 1)
(1 0 1 1 0 1 0 0)
(1 1 1 0 1 1 0 1)
(1 1 1 0 0 1 0 1)
(1 1 0 1 0 1 1 0)
(1 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1326    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1468    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1479    permutation [ 4, 6, 7, 3, 2, 8, 5, 1 ]
vertex  4 -> Algebra 1542    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1504    permutation [ 4, 1, 2, 3, 8, 6, 5, 7 ]
vertex  6 -> Algebra 1526    permutation [ 4, 5, 2, 8, 7, 1, 6, 3 ]
vertex  7 -> Algebra 1353    permutation [ 2, 5, 4, 6, 3, 1, 8, 7 ]
vertex  8 -> Algebra 1540    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1542

Quiver

[ 1, 4 ], [ 2, 4 ], [ 3, 1 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 2 ], [ 6, 3 ], [ 7, 1 ], [ 8, 7 ]

Relations

[ 4, 6, 2 ] 
[ 1, 4, 6, 3 ] 
[ 8, 7, 1, 4 ] 
[ 2, 4, 6 ] 
[ 3, 1, 4, 6 ] 
[ 1, 4, 8, 7 ] 
[ 7, 1, 4, 8 ] 
[ 4, 6, 3, 1 ] - [ 4, 8, 7, 1 ] 
[ 6, 2, 4 ] - [ 6, 3, 1, 4 ] 

Cartan matrix

(1 0 0 1 0 1 0 1)
(0 1 0 1 0 0 1 1)
(1 0 1 1 0 0 0 1)
(1 0 1 1 0 1 1 1)
(1 1 1 1 1 1 0 1)
(1 1 1 1 0 1 0 1)
(1 0 0 1 0 1 1 0)
(1 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1329    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1541    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1494    permutation [ 3, 1, 5, 6, 8, 7, 2, 4 ]
vertex  5 -> Algebra 1538    permutation [ 3, 4, 1, 8, 7, 6, 2, 5 ]
vertex  6 -> Algebra 1525    permutation [ 6, 5, 4, 8, 7, 1, 2, 3 ]
vertex  8 -> Algebra 1571    permutation [ 3, 1, 6, 8, 4, 7, 2, 5 ]

Algebra 1546

Quiver

[ 1, 4 ], [ 1, 7 ], [ 2, 4 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 5 ], [ 8, 7 ]

Relations

[ 7, 5, 1 ] 
[ 1, 4, 3 ] 
[ 3, 1, 4 ] 
[ 6, 4, 5 ] 
[ 8, 7, 5 ] 
[ 4, 5, 6 ] 
[ 7, 5, 8 ] 
[ 4, 3, 1 ] - [ 4, 5, 1 ] 
[ 5, 1, 4 ] - [ 5, 6, 4 ] 
[ 1, 4, 5 ] - [ 1, 7, 5 ] 
[ 5, 1, 7 ] - [ 5, 8, 7 ] 

Cartan matrix

(1 0 0 1 1 0 1 0)
(1 1 1 1 1 0 1 1)
(1 0 1 0 0 0 1 0)
(1 0 1 1 1 0 1 1)
(1 0 0 1 1 1 1 1)
(0 0 1 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1565    permutation [ 5, 2, 6, 3, 4, 1, 8, 7 ]
vertex  2 -> Algebra 1385    permutation [ 5, 1, 6, 3, 2, 7, 8, 4 ]
vertex  3 -> Algebra 1344    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1365    permutation [ 5, 4, 6, 3, 1, 7, 8, 2 ]

Algebra 1550

Quiver

[ 1, 3 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 7, 1 ], [ 7, 8 ]

Relations

[ 3, 4, 5, 6, 7, 1 ] 
[ 4, 5, 6, 7, 1, 3 ] 
[ 5, 6, 7, 1, 3, 4 ] 
[ 6, 7, 1, 3, 4, 5 ] 
[ 7, 1, 3, 4, 5, 6 ] 
[ 1, 3, 4, 5, 6, 7 ] 

Cartan matrix

(1 0 1 1 1 1 0 0)
(1 1 0 1 1 1 1 1)
(0 0 1 1 1 1 1 1)
(1 0 0 1 1 1 1 1)
(1 0 1 0 1 1 1 1)
(1 0 1 1 0 1 1 1)
(1 0 1 1 1 0 1 1)
(0 0 0 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1524    permutation [ 6, 1, 4, 5, 2, 7, 8, 3 ]
vertex  4 -> Algebra 1522    permutation [ 6, 3, 4, 2, 5, 7, 8, 1 ]
vertex  7 -> Algebra 1353    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1573    permutation [ 8, 5, 6, 2, 4, 7, 1, 3 ]

Algebra 1556

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 1 ], [ 5, 7 ], [ 6, 7 ], [ 7, 2 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 3, 4, 2 ] 
[ 4, 2, 3 ] 
[ 1, 2, 5 ] 
[ 7, 2, 5 ] 
[ 2, 5, 7 ] 
[ 1, 2, 8 ] 
[ 4, 2, 8 ] 
[ 2, 5, 1 ] - [ 2, 8, 1 ] 
[ 5, 1, 2 ] - [ 5, 7, 2 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 1 0 0 0)
(1 1 1 0 1 0 1 0)
(0 1 1 1 0 1 1 1)
(0 1 1 1 0 0 1 1)
(1 1 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1565    permutation [ 1, 6, 5, 3, 7, 2, 8, 4 ]
vertex  3 -> Algebra 1418    permutation [ 3, 8, 5, 6, 7, 1, 4, 2 ]
vertex  6 -> Algebra 1466    permutation [ 1, 2, 3, 8, 4, 7, 6, 5 ]
vertex  8 -> Algebra 1373    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1558

Quiver

[ 1, 2 ], [ 1, 3 ], [ 2, 6 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 6, 1 ], [ 6, 7 ], [ 7, 2 ], [ 8, 1 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 3, 8, 1 ] 
[ 8, 1, 3 ] 
[ 2, 8, 4 ] 
[ 1, 2, 6 ] 
[ 7, 2, 6 ] 
[ 2, 6, 7 ] 
[ 4, 2, 8 ] 
[ 2, 6, 1 ] - [ 2, 8, 1 ] 
[ 6, 1, 2 ] - [ 6, 7, 2 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 1, 2, 8 ] - [ 1, 3, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(1 1 0 0 1 1 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 0 1 0 0)
(0 0 0 0 1 0 0 0)
(1 1 1 0 1 1 1 1)
(0 1 0 0 1 0 1 1)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1444    permutation [ 4, 6, 3, 7, 2, 8, 5, 1 ]
vertex  3 -> Algebra 1482    permutation [ 3, 1, 7, 5, 2, 6, 4, 8 ]
vertex  5 -> Algebra 1561    permutation [ 8, 4, 6, 3, 7, 2, 5, 1 ]
vertex  8 -> Algebra 1386    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1561

Quiver

[ 1, 2 ], [ 1, 8 ], [ 2, 6 ], [ 3, 5 ], [ 3, 8 ], [ 4, 1 ], [ 5, 6 ], [ 6, 1 ], [ 6, 3 ], [ 7, 1 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 2, 6, 1 ] 
[ 6, 1, 2 ] 
[ 5, 6, 3 ] 
[ 8, 6, 3 ] 
[ 1, 8, 4 ] 
[ 6, 3, 5 ] 
[ 4, 1, 8 ] 
[ 8, 4, 1 ] - [ 8, 6, 1 ] 
[ 1, 2, 6 ] - [ 1, 8, 6 ] 
[ 3, 5, 6 ] - [ 3, 8, 6 ] 
[ 6, 1, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 1 0 1)
(0 1 1 0 0 1 0 0)
(1 0 1 1 1 1 0 1)
(1 1 0 1 0 0 0 0)
(1 0 0 0 1 1 0 0)
(1 0 1 0 0 1 0 1)
(1 1 0 0 0 1 1 1)
(1 0 0 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1516    permutation [ 7, 6, 3, 5, 8, 2, 4, 1 ]
vertex  4 -> Algebra 1571    permutation [ 4, 8, 1, 5, 6, 3, 2, 7 ]
vertex  7 -> Algebra 1558    permutation [ 8, 6, 4, 2, 7, 3, 5, 1 ]
vertex  8 -> Algebra 1390    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1565

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 5 ], [ 3, 5 ], [ 4, 8 ], [ 5, 6 ], [ 6, 1 ], [ 6, 4 ], [ 7, 8 ], [ 8, 6 ]

Relations

[ 3, 5, 6, 1 ] 
[ 7, 8, 6, 1 ] 
[ 5, 6, 1, 3 ] 
[ 8, 6, 4 ] 
[ 6, 1, 3, 5 ] 
[ 4, 8, 6 ] 
[ 8, 6, 1, 7 ] 
[ 1, 3, 5, 6 ] - [ 1, 7, 8, 6 ] 
[ 6, 1, 7, 8 ] - [ 6, 4, 8 ] 

Cartan matrix

(1 0 1 0 1 1 1 1)
(1 1 0 1 1 1 1 1)
(0 0 1 1 1 1 0 0)
(0 0 0 1 0 0 0 1)
(1 0 0 1 1 1 1 1)
(1 0 1 1 0 1 1 1)
(0 0 0 0 0 1 1 1)
(1 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1556    permutation [ 1, 6, 4, 8, 3, 2, 5, 7 ]
vertex  2 -> Algebra 1539    permutation [ 6, 1, 4, 7, 8, 5, 2, 3 ]
vertex  4 -> Algebra 1414    permutation [ 4, 1, 3, 2, 5, 7, 8, 6 ]
vertex  6 -> Algebra 1546    permutation [ 6, 2, 4, 5, 1, 3, 8, 7 ]

Algebra 1571

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 1 ], [ 3, 7 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 2 ], [ 6, 4 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 2, 5, 3, 1 ] 
[ 1, 2, 5, 3 ] 
[ 7, 5, 3 ] 
[ 5, 6, 4 ] 
[ 2, 5, 6 ] 
[ 4, 5, 6 ] 
[ 5, 3, 7 ] 
[ 5, 3, 1, 2 ] - [ 5, 6, 2 ] 
[ 3, 1, 2, 5 ] - [ 3, 7, 5 ] 
[ 6, 2, 5 ] - [ 6, 4, 5 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 1 0 1 0 0 0)
(1 1 1 0 1 0 1 0)
(1 0 1 1 1 0 0 0)
(1 1 1 0 1 1 0 0)
(0 1 1 1 1 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 1 0 1 0 1 1)

Good mutations

vertex  1 -> Algebra 1561    permutation [ 3, 7, 6, 1, 4, 5, 8, 2 ]
vertex  2 -> Algebra 1523    permutation [ 2, 5, 1, 4, 8, 3, 6, 7 ]
vertex  3 -> Algebra 1463    permutation [ 2, 5, 3, 8, 7, 1, 4, 6 ]
vertex  4 -> Algebra 1542    permutation [ 2, 7, 1, 5, 8, 3, 6, 4 ]
vertex  7 -> Algebra 1540    permutation [ 2, 4, 1, 7, 8, 3, 6, 5 ]
vertex  8 -> Algebra 1482    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1573

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 5, 2 ], [ 6, 7 ], [ 7, 8 ], [ 8, 5 ]

Relations

[ 3, 6, 7, 8, 5, 2 ] 
[ 6, 7, 8, 5, 2, 3 ] 
[ 2, 3, 6, 7, 8, 5 ] 
[ 7, 8, 5, 2, 3, 6 ] 
[ 8, 5, 2, 3, 6, 7 ] 
[ 5, 2, 3, 6, 7, 8 ] 

Cartan matrix

(1 1 0 0 1 1 1 1)
(0 1 1 0 0 1 1 1)
(0 0 1 0 1 1 1 1)
(0 1 1 1 1 1 1 0)
(0 1 1 0 1 1 1 0)
(0 1 0 0 1 1 1 1)
(0 1 1 0 1 0 1 1)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1550    permutation [ 7, 4, 8, 5, 2, 3, 6, 1 ]
vertex  4 -> Algebra 1550    permutation [ 2, 1, 3, 6, 7, 8, 5, 4 ]
vertex  5 -> Algebra 1540    permutation [ 8, 4, 7, 3, 1, 6, 5, 2 ]
vertex  6 -> Algebra 1540    permutation [ 3, 1, 2, 8, 4, 5, 6, 7 ]