# The 16 transitive groups of degree 6 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..6 ; name
6 ; 3,4,5,6,1,2 6,1,2,3,4,5 ; C(6) = 6 = 3[x]2
6 ; 3,4,5,6,1,2 2,1,6,5,4,3 ; D_6(6) = [3]2
12 ; 3,4,5,6,1,2 1,6,5,4,3,2 6,1,2,3,4,5 ; D(6) = S(3)[x]2
12 ; 1,3,2,5,4,6 6,2,3,5,4,1 3,4,5,6,1,2 ; A_4(6) = [2^2]3
18 ; 3,4,5,6,1,2 2,1,6,5,4,3 1,4,3,6,5,2 ; F_18(6) = [3^2]2 = 3 wr 2
24 ; 6,3,2,5,4,1 6,2,3,4,5,1 1,2,3,5,4,6 5,1,6,2,3,4 ; 2A_4(6) = [2^3]3 = 2 wr 3
24 ; 1,3,2,5,4,6 6,2,3,5,4,1 3,4,5,6,1,2 1,5,4,3,2,6 ; S_4(6d) = [2^2]S(3)
24 ; 1,3,2,5,4,6 6,2,3,5,4,1 3,4,5,6,1,2 3,6,1,5,4,2 ; S_4(6c) = 1/2[2^3]S(3)
36 ; 3,4,5,6,1,2 2,1,6,5,4,3 1,4,3,6,5,2 6,1,2,3,4,5 ; F_18(6):2 = [1/2.S(3)^2]2
36 ; 3,4,5,6,1,2 1,4,3,6,5,2 1,6,5,4,3,2 6,3,4,5,2,1 ; F_36(6) = 1/2[S(3)^2]2
48 ; 6,3,2,5,4,1 6,2,3,4,5,1 1,2,3,5,4,6 5,1,6,2,3,4 3,6,1,5,4,2 ; 2S_4(6) = [2^3]S(3) = 2 wr S(3)
60 ; 1,3,2,5,4,6 3,5,6,2,4,1 ; L(6) = PSL(2,5) = A_5(6)
72 ; 3,4,5,6,1,2 2,1,6,5,4,3 1,4,3,6,5,2 6,1,2,3,4,5 5,2,3,4,1,6 ; F_36(6):2 = [S(3)^2]2 = S(3) wr 2
120 ; 1,3,2,5,4,6 3,5,6,2,4,1 4,1,5,6,2,3 ; L(6):2 = PGL(2,5) = S_5(6)
360 ; 1,3,2,5,4,6 5,1,6,2,4,3 ; A6
720 ; 1,3,2,5,4,6 5,1,6,2,4,3 2,1,3,4,5,6 ; S6
