[GAP Forum] Transitive groups

[Alexander Hulpke]

Dear Forum,

Marek Mitros asked:
> 
> But when I use function TransitiveGroup(n,s) then I see following
> 
>   tn:=NrTransitiveGroups(n);
>   g:=List([1..tn], s->TransitiveGroup(n,s));
>   Print("In dimesion", n, " there are ",tn," transitive groups. \n");
>   Print(g, "\n");
>   sg:=List(g, x->Size(x));
>   Print("Sizes are: ",sg, "\n");
> 
> In dimesion6 there are 16 transitive groups. 
> [ C(6) = 6 = 3[x]2, D_6(6) = [3]2, D(6) = S(3)[x]2, A_4(6) = [2^2]3, 
>  F_18(6) = [3^2]2 = 3 wr 2, 2A_4(6) = [2^3]3 = 2 wr 3, S_4(6d) = [2^2]S(3), 
>  S_4(6c) = 1/2[2^3]S(3), F_18(6):2 = [1/2.S(3)^2]2, F_36(6) = 1/2[S(3)^2]2, 
>  2S_4(6) = [2^3]S(3) = 2 wr S(3), L(6) = PSL(2,5) = A_5(6), 
>  F_36(6):2 = [S(3)^2]2 = S(3) wr 2, L(6):2 = PGL(2,5) = S_5(6), A6, S6 ]
> Sizes are: [ 6, 6, 12, 12, 18, 24, 24, 24, 36, 36, 48, 60, 72, 120, 360, 720 ]
> 
> Where I can find explanation of the notation A_4(6), F_18(6), in other dimension there are also F(5), E(9), etc. ?

The names are defined in:

MR1635715 (99g:20011) 
Conway, John H.(1-PRIN); Hulpke, Alexander(4-STAN-SM); McKay, John(3-CONC-AL)
On transitive permutation groups.
LMS J. Comput. Math. 1 (1998), 1--8

The extra information in parentheses provides information about the permutation structure.

Best,

   Alexander Hulpke




-- Colorado State University, Department of Mathematics,
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