# The 34 transitive groups of degree 9 up to conjugacy, computed by sagebrush-group
# (src/transitive.rs, from scratch).  Line k is the group nTk: the standard numbering
# and the names (last field) were matched against GAP's transitive groups library,
# used as an oracle (examples/label_tables.rs).  Per line:
# order ; generators as image lists of 1..9 ; name
9 ; 7,8,4,9,1,2,5,6,3 9,1,2,8,4,5,3,7,6 ; C(9)=9
9 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 ; E(9)=3[x]3
18 ; 7,8,4,9,1,2,5,6,3 9,1,2,8,4,5,3,7,6 7,3,2,6,5,4,1,9,8 ; D(9)=9:2
18 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 7,8,4,2,6,9,3,1,5 ; S(3)[x]3
18 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 5,9,6,8,1,3,7,4,2 ; S(3)[1/2]S(3)=3^2:2
27 ; 7,8,4,9,1,2,5,6,3 7,2,9,3,1,6,5,8,4 9,1,2,8,4,5,3,7,6 ; 1/3[3^3]3
27 ; 7,8,4,9,1,2,5,6,3 7,2,9,3,1,6,5,8,4 4,7,8,6,3,1,9,5,2 ; E(9):3=[3^2]3
36 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 5,9,6,8,1,3,7,4,2 7,8,4,2,6,9,3,1,5 ; S(3)[x]S(3)=E(9):D_4
36 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 5,9,6,8,1,3,7,4,2 1,7,5,9,2,8,3,4,6 ; E(9):4
54 ; 7,8,4,9,1,2,5,6,3 7,2,9,3,1,6,5,8,4 9,1,2,8,4,5,3,7,6 4,2,7,1,9,8,3,6,5 ; [3^2]S(3)_6
54 ; 7,8,4,9,1,2,5,6,3 7,2,9,3,1,6,5,8,4 4,7,8,6,3,1,9,5,2 4,2,7,1,9,8,3,6,5 ; E(9):6=1/2[3^2:2]S(3)
54 ; 7,8,4,9,1,2,5,6,3 7,2,9,3,1,6,5,8,4 4,7,8,6,3,1,9,5,2 5,9,6,2,7,4,1,3,8 ; [3^2]S(3)
54 ; 7,8,4,9,1,2,5,6,3 7,2,9,3,1,6,5,8,4 4,7,8,6,3,1,9,5,2 3,7,2,6,4,5,9,1,8 ; E(9):D_6=[3^2:2]3=[1/2.S(3)^2]3
72 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 5,9,6,8,1,3,7,4,2 1,7,5,9,2,8,3,4,6 5,3,8,9,4,6,2,7,1 ; M(9)=E(9):Q_8
72 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 5,9,6,8,1,3,7,4,2 1,7,5,9,2,8,3,4,6 8,1,9,7,5,4,3,6,2 ; E(9):8
72 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 5,9,6,8,1,3,7,4,2 1,7,5,9,2,8,3,4,6 7,8,4,3,5,6,1,2,9 ; E(9):D_8
81 ; 1,2,3,9,5,6,4,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 7,5,8,2,4,1,6,9,3 ; [3^3]3=3wr3
108 ; 7,8,4,9,1,2,5,6,3 7,2,9,3,1,6,5,8,4 4,7,8,6,3,1,9,5,2 4,2,7,1,9,8,3,6,5 3,5,2,6,4,1,9,7,8 ; E(9):D_12=[3^2:2]S(3)=[1/2.S(3)^2]S(3)
144 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 5,9,6,8,1,3,7,4,2 1,7,5,9,2,8,3,4,6 5,3,8,9,4,6,2,7,1 4,9,3,7,2,8,5,1,6 ; E(9):2D_8
162 ; 1,2,3,9,5,6,4,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 7,5,8,2,4,1,6,9,3 2,1,5,7,3,8,9,6,4 ; [3^3]S(3)=3wrS(3)
162 ; 1,2,3,9,5,6,4,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 7,5,8,2,4,1,6,9,3 9,6,3,5,4,2,8,7,1 ; 1/2.[3^3:2]S(3)
162 ; 1,2,3,9,5,6,4,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 1,2,6,4,8,3,9,5,7 2,9,7,5,6,4,1,3,8 ; [3^3:2]3
216 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 5,9,6,8,1,3,7,4,2 1,7,5,9,2,8,3,4,6 5,3,8,9,4,6,2,7,1 4,9,3,8,1,7,6,2,5 ; E(9):2A_4
324 ; 1,2,3,9,5,6,4,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 1,2,6,4,8,3,9,5,7 2,9,7,5,6,4,1,3,8 9,3,2,5,7,6,1,4,8 ; [3^3:2]S(3)
324 ; 1,2,3,9,5,6,4,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 8,3,6,9,5,2,7,1,4 8,2,6,4,1,3,9,5,7 7,5,8,2,4,1,6,9,3 ; [1/2.S(3)^3]3
432 ; 7,8,4,9,1,2,5,6,3 4,7,8,6,3,1,9,5,2 5,9,6,8,1,3,7,4,2 1,7,5,9,2,8,3,4,6 5,3,8,9,4,6,2,7,1 4,9,3,8,1,7,6,2,5 4,9,3,7,2,8,5,1,6 ; E(9):2S_4
504 ; 1,6,7,8,9,2,3,4,5 4,6,1,2,3,9,7,8,5 ; L(9)=PSL(2,8)
648 ; 1,2,3,9,5,6,4,8,7 1,2,3,4,5,6,9,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 1,2,6,4,8,3,9,5,7 8,2,3,4,5,6,7,1,9 2,9,7,5,6,4,1,3,8 ; [S(3)^3]3=S(3)wr3
648 ; 1,2,3,9,5,6,4,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 8,3,6,9,5,2,7,1,4 8,2,6,4,1,3,9,5,7 7,5,8,2,4,1,6,9,3 2,8,1,9,6,5,7,3,4 ; [1/2.S(3)^3]S(3)
648 ; 1,2,3,9,5,6,4,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 8,3,6,9,5,2,7,1,4 8,2,6,4,1,3,9,5,7 7,5,8,2,4,1,6,9,3 9,3,2,5,7,6,1,4,8 ; 1/2[S(3)^3]S(3)
1296 ; 1,2,3,9,5,6,4,8,7 1,2,3,4,5,6,9,8,7 5,6,2,4,8,3,7,1,9 8,6,2,4,1,3,7,5,9 1,2,6,4,8,3,9,5,7 8,2,3,4,5,6,7,1,9 2,9,7,5,6,4,1,3,8 2,8,1,9,6,5,7,3,4 ; [S(3)^3]S(3)=S(3)wrS(3)
1512 ; 1,6,7,8,9,2,3,4,5 4,6,1,2,3,9,7,8,5 2,5,7,1,6,8,3,4,9 ; L(9):3=P|L(2,8)
181440 ; 1,6,7,8,9,2,3,4,5 3,1,4,5,6,7,8,9,2 ; A9
362880 ; 1,6,7,8,9,2,3,4,5 3,1,4,5,6,7,8,9,2 2,1,3,4,5,6,7,8,9 ; S9
