# The 45 transitive groups of degree 10 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..10 ; name
10 ; 2,1,4,3,6,5,8,7,10,9 5,6,1,2,7,8,9,10,3,4 ; C(10)=5[x]2
10 ; 5,6,1,2,7,8,9,10,3,4 8,7,10,9,6,5,2,1,4,3 ; D(10)=5:2
20 ; 2,1,4,3,6,5,8,7,10,9 5,6,1,2,7,8,9,10,3,4 8,7,10,9,6,5,2,1,4,3 ; D_10(10)=[D(5)]2
20 ; 5,6,1,2,7,8,9,10,3,4 7,8,9,10,5,6,1,2,3,4 10,9,6,5,2,1,8,7,4,3 ; 1/2[F(5)]2
40 ; 2,1,4,3,6,5,8,7,10,9 5,6,1,2,7,8,9,10,3,4 8,7,10,9,6,5,2,1,4,3 10,9,6,5,2,1,8,7,4,3 ; F(5)[x]2
50 ; 3,1,5,2,4,10,9,6,8,7 6,10,8,7,9,1,4,3,5,2 4,5,2,3,1,6,7,8,9,10 ; [5^2]2
60 ; 5,1,6,7,2,8,9,3,4,10 5,6,7,1,8,9,2,10,3,4 ; A_5(10)
80 ; 1,2,4,3,6,5,8,7,10,9 2,1,3,4,5,6,7,8,10,9 1,2,3,4,6,5,7,8,10,9 1,2,3,4,5,6,8,7,10,9 5,6,1,2,7,8,9,10,3,4 ; [2^4]5
100 ; 3,1,5,2,4,10,9,6,8,7 6,10,8,7,9,1,4,3,5,2 4,5,2,3,1,6,7,8,9,10 9,7,8,10,6,1,5,2,4,3 ; [1/2.D(5)^2]2
100 ; 3,1,5,2,4,10,9,6,8,7 4,5,2,3,1,6,7,8,9,10 2,1,4,3,5,8,7,6,10,9 10,8,9,7,6,1,2,4,3,5 ; 1/2[D(5)^2]2
120 ; 1,2,7,8,9,10,3,4,5,6 5,6,1,2,7,8,9,10,3,4 4,3,8,7,2,1,10,9,6,5 ; A(5)[x]2
120 ; 1,2,7,8,9,10,3,4,5,6 5,6,1,2,7,8,9,10,3,4 2,1,8,7,4,3,10,9,6,5 ; 1/2[S(5)]2=S_5(10a)
120 ; 1,5,6,7,2,3,4,8,9,10 5,6,7,1,8,9,2,10,3,4 ; S_5(10d)
160 ; 2,1,4,3,6,5,8,7,10,9 1,2,3,4,6,5,7,8,10,9 1,2,3,4,5,6,7,8,10,9 2,1,3,4,5,6,7,8,9,10 1,2,3,4,5,6,8,7,10,9 5,6,1,2,7,8,9,10,3,4 ; [2^5]5
160 ; 1,2,4,3,6,5,8,7,10,9 2,1,3,4,5,6,7,8,10,9 1,2,3,4,6,5,7,8,10,9 1,2,3,4,5,6,8,7,10,9 5,6,1,2,7,8,9,10,3,4 7,8,9,10,6,5,1,2,4,3 ; [2^4]D(5)
160 ; 1,2,4,3,6,5,8,7,10,9 2,1,3,4,5,6,7,8,10,9 1,2,3,4,6,5,7,8,10,9 1,2,3,4,5,6,8,7,10,9 5,6,1,2,7,8,9,10,3,4 8,7,9,10,6,5,1,2,4,3 ; 1/2[2^5]D(5)
200 ; 3,1,5,2,4,10,9,6,8,7 6,10,8,7,9,1,4,3,5,2 4,5,2,3,1,6,7,8,9,10 9,7,8,10,6,1,5,2,4,3 10,8,9,7,6,1,2,4,3,5 ; [5^2:4]2
200 ; 3,1,5,2,4,10,9,6,8,7 4,5,2,3,1,6,7,8,9,10 2,1,4,3,5,8,7,6,10,9 3,2,4,5,1,10,6,8,7,9 7,9,10,8,6,1,2,4,3,5 ; [5^2:4]2_2
200 ; 3,1,5,2,4,10,9,6,8,7 6,10,8,7,9,1,4,3,5,2 4,5,2,3,1,6,7,8,9,10 9,7,8,10,6,1,5,2,4,3 8,10,7,9,6,1,2,4,3,5 ; [5^2:4_2]2
200 ; 3,1,5,2,4,10,9,6,8,7 4,5,2,3,1,6,7,8,9,10 2,1,4,3,5,8,7,6,10,9 4,1,3,5,2,10,6,8,7,9 10,8,9,7,6,1,2,4,3,5 ; [5^2:4_2]2_2
200 ; 3,1,5,2,4,10,9,6,8,7 6,10,8,7,9,1,4,3,5,2 4,5,2,3,1,6,7,8,9,10 9,7,8,10,6,1,5,2,4,3 3,5,1,4,2,10,9,6,8,7 ; [D(5)^2]2
240 ; 1,2,7,8,9,10,3,4,5,6 5,6,1,2,7,8,9,10,3,4 4,3,8,7,2,1,10,9,6,5 3,4,1,2,5,6,7,8,9,10 ; S(5)[x]2
320 ; 2,1,4,3,6,5,8,7,10,9 1,2,3,4,6,5,7,8,10,9 1,2,3,4,5,6,7,8,10,9 2,1,3,4,5,6,7,8,9,10 1,2,3,4,5,6,8,7,10,9 5,6,1,2,7,8,9,10,3,4 7,8,9,10,6,5,1,2,4,3 ; [2^5]D(5)
320 ; 1,2,4,3,6,5,8,7,10,9 2,1,3,4,5,6,7,8,10,9 1,2,3,4,6,5,7,8,10,9 1,2,3,4,5,6,8,7,10,9 5,6,1,2,7,8,9,10,3,4 7,8,9,10,6,5,1,2,4,3 1,2,8,7,9,10,6,5,3,4 ; [2^4]F(5)
320 ; 1,2,4,3,6,5,8,7,10,9 2,1,3,4,5,6,7,8,10,9 1,2,3,4,6,5,7,8,10,9 1,2,3,4,5,6,8,7,10,9 5,6,1,2,7,8,9,10,3,4 7,8,9,10,6,5,1,2,4,3 2,1,8,7,9,10,6,5,3,4 ; 1/2[2^5]F(5)
360 ; 2,3,1,5,6,4,8,9,7,10 10,3,2,9,7,6,5,8,4,1 1,8,6,9,4,2,5,3,7,10 ; L(10)=PSL(2,9)
400 ; 3,1,5,2,4,10,9,6,8,7 6,10,8,7,9,1,4,3,5,2 4,5,2,3,1,6,7,8,9,10 9,7,8,10,6,1,5,2,4,3 3,5,1,4,2,10,9,6,8,7 8,10,7,9,6,1,2,4,3,5 ; [1/2.F(5)^2]2
400 ; 3,1,5,2,4,10,9,6,8,7 4,5,2,3,1,6,7,8,9,10 2,1,4,3,5,8,7,6,10,9 3,2,4,5,1,10,6,8,7,9 3,5,1,4,2,10,9,6,8,7 7,9,10,8,6,1,2,4,3,5 ; 1/2[F(5)^2]2
640 ; 2,1,4,3,6,5,8,7,10,9 1,2,3,4,6,5,7,8,10,9 1,2,3,4,5,6,7,8,10,9 2,1,3,4,5,6,7,8,9,10 1,2,3,4,5,6,8,7,10,9 5,6,1,2,7,8,9,10,3,4 7,8,9,10,6,5,1,2,4,3 1,2,8,7,9,10,6,5,3,4 ; [2^5]F(5)
720 ; 2,3,1,5,6,4,8,9,7,10 10,3,2,9,7,6,5,8,4,1 1,8,6,9,4,2,5,3,7,10 1,4,7,8,2,5,6,9,3,10 ; L(10):2=PGL(2,9)
720 ; 2,3,1,5,6,4,8,9,7,10 10,3,2,9,7,6,5,8,4,1 1,8,6,9,4,2,5,3,7,10 1,4,7,3,6,9,2,5,8,10 ; M(10)=L(10)'2
720 ; 2,3,1,5,6,4,8,9,7,10 10,3,2,9,7,6,5,8,4,1 1,8,6,9,4,2,5,3,7,10 1,2,3,9,7,8,5,6,4,10 ; S_6(10)=L(10):2
800 ; 3,1,5,2,4,10,9,6,8,7 6,10,8,7,9,1,4,3,5,2 4,5,2,3,1,6,7,8,9,10 9,7,8,10,6,1,5,2,4,3 3,5,1,4,2,10,9,6,8,7 8,10,7,9,6,1,2,4,3,5 7,9,10,8,6,1,2,4,3,5 ; [F(5)^2]2
960 ; 1,2,7,8,9,10,3,4,5,6 3,4,8,7,9,10,6,5,1,2 ; [2^4]A(5)
1440 ; 2,3,1,5,6,4,8,9,7,10 10,3,2,9,7,6,5,8,4,1 1,8,6,9,4,2,5,3,7,10 1,4,7,8,2,5,6,9,3,10 1,2,3,9,7,8,5,6,4,10 ; L(10).2^2=P|L(2,9)
1920 ; 1,2,7,8,9,10,3,4,5,6 3,4,8,7,9,10,6,5,1,2 2,1,3,4,5,6,7,8,9,10 ; [2^5]A(5)
1920 ; 1,2,7,8,9,10,3,4,5,6 3,4,8,7,9,10,6,5,1,2 3,4,1,2,5,6,7,8,9,10 ; [2^4]S(5)
1920 ; 1,2,7,8,9,10,3,4,5,6 3,4,8,7,9,10,6,5,1,2 4,3,1,2,5,6,7,8,9,10 ; 1/2[2^5]S(5)
3840 ; 1,2,7,8,9,10,3,4,5,6 3,4,8,7,9,10,6,5,1,2 4,3,1,2,5,6,7,8,9,10 2,1,3,4,5,6,7,8,9,10 ; [2^5]S(5)
7200 ; 4,5,3,1,2,10,9,8,7,6 5,1,2,3,4,6,7,10,8,9 6,7,8,9,10,1,2,3,4,5 ; [A(5)^2]2
14400 ; 4,5,3,1,2,10,9,8,7,6 5,1,2,3,4,6,7,10,8,9 1,2,5,4,3,10,8,9,7,6 6,7,8,9,10,1,2,3,4,5 ; [1/2.S(5)^2]2=[A(5):2]2
14400 ; 4,5,3,1,2,10,9,8,7,6 5,1,2,3,4,6,7,10,8,9 1,2,5,4,3,10,8,9,7,6 7,6,8,9,10,1,2,3,4,5 ; 1/2[S(5)^2]2
28800 ; 4,5,3,1,2,10,9,8,7,6 5,1,2,3,4,6,7,10,8,9 1,2,5,4,3,10,8,9,7,6 7,6,8,9,10,1,2,3,4,5 2,1,3,4,5,6,7,8,9,10 ; [S(5)^2]2
1814400 ; 2,3,1,4,5,6,7,8,9,10 1,3,4,5,6,7,8,9,10,2 ; A10
3628800 ; 2,1,3,4,5,6,7,8,9,10 2,3,4,5,6,7,8,9,10,1 ; S10
