Iterating over automorphism group in Magma

Question

I am trying to iterate over the automorphism group of a group but Magma keeps telling me that "Iteration is not possible over this object." Does anyone know a workaround for this?

This is what I tried to input:

G:=DihedralGroup(32);
N:=NormalSubgroups(G);
Q:=G/N[2]`subgroup;
A:=AutomorphismGroup(Q);
Type(A);
for x in A do
    for y in Q do
        x(y);
    end for;
end for;

Magma does give me the set of generators for the automorphism group and the cardinality of the automorphism group. So I guess a dumb workaround would be to use that to recreate the group as a list. However, I do not know of an efficient way to do that

Answer 1

One thing you could do is to set $P,f:=$PCGroup$(A)$ and then iterate on $P$ making its element act on $G$ via $f^{-1}$.

(I hope this is still useful to someone, if not to you!)