There are a couple of ways to do it:
--------------------------------------------
n:=3;; # or whatever value you wish
G:=DihedralGroup(2*n);
RG:=Action(G,Elements(G),OnRight); # basically the right regular representation
AutG:=Action(AutomorphismGroup(G),Elements(G));
--------------------------------------------
Alternately, you can do this:
--------------------------------------------
n:=3;;
G:=DihedralGroup(2*n);
RG:=Action(G,Elements(G),OnRight); # basically the right regular representation
HolG:=Normalizer(SymmetricGroup(2*n),RG);;
AutG:=AsGroup(Filtered(Elements(HolG),g->OnPoints(1,g)=1));;
--------------------------------------------
which is a bit more computationally intensive as n increases because
one is filtering the elements of a group (the holomorph).
However, it's nice in that it is a manifestation of one of the classic
definitions of the automorphism group, namely as the set of those elements
(permutations of G as a set) which normalize the right (or left) regular
represenation and fix the identity, which of course the automorphism group
*must* do.
(Note, the ambient symmetric group these are embedded in is not Perm(G)
but rather S_{2n}, so one is tacitly identifying '1' with 'e_G' the identity
of G.)
-Tim K.
On Tue, 19 Jul 2016, abdulhakeem alayiwola wrote:
> I am more interested in the procedure than the result. If anyone can help
> we the procedure or steps to find Aut(D2n) using GAP. I will be very glad
> on any hint as well.
> Regards
>
> On Jul 18, 2016 4:56 PM, "abdulhakeem alayiwola" <lovepgro...@gmail.com>
> wrote:
>
> > Dear forum,
> > Can anyone in the house describe the steps to find Aut(D2n) using GAP.
> > Note that Aut(D2n) is Automorphism group of Dihedral group of order 2n.
> > Regards.
> >
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