Semidirect product of groups by magma

Question

Can anybody guide me towards, how I can compute semidirect product of $\mathrm{PSL}(3,4)$ and $\mathbb Z_2$ by magma? Indeed, I dont know how construct map $\phi: H \to \mathrm{Aut}(N)$, when $H=\mathbb Z_2$ and $N=\mathrm{PSL}(3,4)$, for operation SemidirectProduct$(N, H, \phi)$.

Answer 1

Here's one way to do it.

K:=PSL(3,4);
H:=CyclicGroup(2);
A:=AutomorphismGroup(K);
/* A.1 is an automorphism of order 2 */
phi:= hom< H -> A | <H.1,A.1> >;
G:=SemidirectProduct(K,H,phi);

Notice that the codomain of phi is A, which has type GrpAuto. I'm not sure if this is a requirement of the map or not.