[GAP Forum] regular subgroups of the Symmetric Group S_24 isomorphic to S_4.

[Alejandra Alderete]

Dear Forum,

Can you help me??

I need to work with groups of hight order and my computer isn't  potency o
capacity , I don't  know. I am sending the algorithm. I need to find the
regular subgroups of the Symmetric Group  S_24  isomorphic to S_4.

gap> s4 := SymmetricGroup (4);
gap> s24 := SymmetricGroup (24);
gap> homo := AllHomomorphisms (s4, s24);;
gap> inj :=Filtered (homo, function (v) return IsInjective (v)= true ; end);
gap> img := List (inj, x-> Image (x, s4));
gap> reg := Filtered (img, function (v) return IsRegular(v)= true ; end);



best regards

Alejandra