For example if we let
G:= Sym(6);
A:= AutomorphismGroup(G);
P:= PermutationGroup(A);
I:= {@ i : i in G | Order(i) eq 2 @};
then how does one construct the G-set that has the P acting on I by the map the shows how the automorphisms permute the involutions?
I'm new to MAGMA but I have speant a lot of time reading the handbook lately and I have not found any way to do this. Does anyone have any helpful suggestions?