# The 50 transitive groups of degree 8 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..8 ; name
8 ; 2,1,6,7,8,3,4,5 3,6,2,8,4,1,5,7 4,7,8,6,2,5,3,1 ; C(8)=8
8 ; 2,1,6,7,8,3,4,5 3,6,2,8,4,1,5,7 4,7,8,2,3,5,1,6 ; 4[x]2
8 ; 2,1,6,7,8,3,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 ; E(8)=2[x]2[x]2
8 ; 2,1,6,7,8,3,4,5 3,6,2,8,4,1,5,7 7,4,8,2,6,5,1,3 ; D_8(8)=[4]2
8 ; 2,1,6,7,8,3,4,5 3,6,2,8,4,1,5,7 5,8,7,3,2,4,6,1 ; Q_8(8)
16 ; 2,1,6,7,8,3,4,5 3,6,2,8,4,1,5,7 7,4,8,2,6,5,1,3 6,3,2,7,5,1,4,8 ; D(8)
16 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 4,7,8,2,3,5,1,6 5,8,2,3,4,1,6,7 ; 1/2[2^3]4
16 ; 2,1,6,7,8,3,4,5 3,6,2,8,4,1,5,7 5,8,7,3,2,4,6,1 5,8,6,4,1,3,7,2 ; 2D_8(8)=[D(4)]2
16 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,8,2,6,5,1,3 3,6,1,5,4,2,8,7 ; E(8):2=D(4)[x]2
16 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,8,2,6,5,1,3 5,8,1,6,7,2,3,4 ; [2^2]4
16 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 4,7,8,2,3,5,1,6 3,6,1,5,4,2,8,7 ; 1/2[2^3]E(4)=Q_8:2
24 ; 2,1,6,7,8,3,4,5 3,6,2,8,4,1,5,7 5,8,7,3,2,4,6,1 2,1,5,3,7,8,6,4 ; 2A_4(8)=[2]A(4)=SL(2,3)
24 ; 2,1,6,7,8,3,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 2,1,5,3,7,8,6,4 ; E(8):3=A(4)[x]2
24 ; 2,1,6,7,8,3,4,5 3,6,1,5,4,2,8,7 6,1,3,5,8,2,7,4 5,4,8,3,6,7,1,2 ; S(4)[1/2]2=1/2(S_4[x]2)
32 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 4,7,8,2,3,5,1,6 3,6,1,5,4,2,8,7 5,8,2,3,4,1,6,7 ; [1/4.cD(4)^2]2
32 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 5,8,7,1,3,4,2,6 ; 1/2[2^4]4
32 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 4,7,8,2,3,5,1,6 7,4,3,1,5,6,2,8 5,8,2,3,4,1,6,7 ; [4^2]2
32 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,3,2,5,6,1,8 7,4,8,2,6,5,1,3 5,8,1,6,7,2,3,4 ; E(8):E_4=[2^2]D(4)
32 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,8,2,6,5,1,3 7,4,6,1,5,3,2,8 5,8,1,6,7,2,3,4 ; E(8):4=[1/4.eD(4)^2]2
32 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 5,8,4,2,6,7,1,3 ; [2^3]4
32 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 4,7,5,1,6,8,2,3 ; 1/2[2^4]E(4)=[1/4.dD(4)^2]2
32 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 ; E(8):D_4=[2^3]2^2
48 ; 2,1,6,7,8,3,4,5 3,6,2,8,4,1,5,7 5,8,7,3,2,4,6,1 2,1,5,3,7,8,6,4 4,7,6,1,5,3,2,8 ; 2S_4(8)=GL(2,3)
48 ; 2,1,6,7,8,3,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 2,1,5,3,7,8,6,4 4,7,2,8,3,1,5,6 ; E(8):D_6=S(4)[x]2
56 ; 2,1,6,7,8,3,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 4,6,2,7,1,5,3,8 ; E(8):7=F_56(8)
64 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 5,8,2,3,4,1,6,7 ; 1/2[2^4]eD(4)
64 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 5,8,7,1,3,4,2,6 2,1,3,4,5,6,7,8 ; [2^4]4
64 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 4,7,5,1,6,8,2,3 6,3,1,4,8,2,7,5 ; 1/2[2^4]dD(4)
64 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 5,8,4,2,6,7,1,3 ; E(8):D_8=[2^3]D(4)
64 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 4,7,5,1,6,8,2,3 5,8,4,2,6,7,1,3 ; 1/2[2^4]cD(4)
64 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 2,1,3,4,5,6,7,8 ; [2^4]E(4)
96 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 2,1,5,3,7,8,6,4 ; [2^3]A(4)
96 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,3,2,5,6,1,8 7,4,8,2,6,5,1,3 7,1,3,4,6,8,2,5 6,3,7,8,2,4,5,1 ; E(8):A_4=[1/3.A(4)^2]2=E(4):6
96 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,3,2,5,6,1,8 7,4,8,2,6,5,1,3 7,1,3,4,6,8,2,5 5,8,1,6,7,2,3,4 ; 1/2[E(4)^2:S_3]2=E(4)^2:D_6
128 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 5,8,4,2,6,7,1,3 2,1,3,4,5,6,7,8 ; [2^4]D(4)
168 ; 2,1,6,7,8,3,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 4,6,2,7,1,5,3,8 2,8,4,6,5,3,7,1 ; E(8):F_21
168 ; 2,1,6,7,8,3,4,5 5,4,7,1,2,3,8,6 ; L(8)=PSL(2,7)
192 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 2,1,5,3,7,8,6,4 2,1,3,4,5,6,7,8 ; [2^4]A(4)
192 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 2,1,5,3,7,8,6,4 5,8,4,2,6,7,1,3 ; [2^3]S(4)
192 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 2,1,5,3,7,8,6,4 5,8,2,3,4,1,6,7 ; 1/2[2^4]S(4)
192 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,3,2,5,6,1,8 7,4,8,2,6,5,1,3 7,1,3,4,6,8,2,5 1,7,5,4,6,8,2,3 5,8,1,6,7,2,3,4 ; E(8):S_4=[E(4)^2:S_3]2=E(4)^2:D_12
288 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,3,2,5,6,1,8 7,4,8,2,6,5,1,3 7,1,3,4,6,8,2,5 5,8,1,6,7,2,3,4 7,2,6,1,8,3,4,5 ; [A(4)^2]2
336 ; 2,1,6,7,8,3,4,5 5,4,7,1,2,3,8,6 6,3,2,7,5,1,4,8 ; L(8):2=PGL(2,7)
384 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 1,2,3,7,8,6,4,5 3,6,1,5,4,2,8,7 7,4,8,2,6,5,1,3 2,1,5,3,7,8,6,4 5,8,4,2,6,7,1,3 2,1,3,4,5,6,7,8 ; [2^4]S(4)
576 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,3,2,5,6,1,8 7,4,8,2,6,5,1,3 7,1,3,4,6,8,2,5 5,8,1,6,7,2,3,4 7,2,6,1,8,3,4,5 6,3,7,8,2,4,5,1 ; [1/2.S(4)^2]2
576 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,3,2,5,6,1,8 7,4,8,2,6,5,1,3 7,1,3,4,6,8,2,5 7,2,6,1,8,3,4,5 1,7,5,4,6,8,2,3 5,8,2,3,4,1,6,7 ; 1/2[S(4)^2]2
1152 ; 2,1,6,7,8,3,4,5 2,1,3,7,5,6,4,8 7,4,3,2,5,6,1,8 7,4,8,2,6,5,1,3 7,1,3,4,6,8,2,5 5,8,1,6,7,2,3,4 7,2,6,1,8,3,4,5 6,3,7,8,2,4,5,1 2,1,3,4,5,6,7,8 ; [S(4)^2]2
1344 ; 1,8,6,4,5,3,7,2 4,1,7,5,2,3,8,6 ; E(8):L_7=AL(8)
20160 ; 1,8,6,4,5,3,7,2 2,1,5,3,7,8,6,4 ; A8
40320 ; 1,8,6,4,5,3,7,2 2,1,5,3,7,8,6,4 2,1,3,4,5,6,7,8 ; S8
