I am newbie in the GAP and in the group theory. Now I am trying to make semidirect product if GL(3,2) and GL(3,2) inversed and transposed. I use code below
H:=GeneralLinearGroup(3, 2); GH:=GeneratorsOfGroup(H); GT:=List(GH, g->Inverse(TransposedMat(g))); T:=Group(GT); A:=AutomorphismGroup(T); elts := Elements(A); map:=GroupHomomorphismByImages(H, A,GeneratorsOfGroup(H), [elts, elts]); SemidirectProduct(T,map,H);
I got error about "GroupHomomorphismByImages" failed. I have no idea what should I do. From related topics I got that I should define proper homomorphism. But I cannot imagine what is possible here.
I will be very thankful if you help me to solve this issue.