How to obtain elements of dihedral group in GAP

Question

I'd like to obtain a list of all permutations contained in D_n using GAP. E.g. for D_8 I've tried the following:

gap> G := DihedralGroup(8);
<pc group of size 8 with 3 generators>
gap> List(G);
[ <identity> of ..., f3, f2, f2*f3, f1, f1*f3, f1*f2, f1*f2*f3 ]

How can I obtain a list of actual permutations contained in D_8 instead?

Answer 1

maybe you could try this:

gap> D_8:=DihedralGroup(IsPermGroup,8);
Group([ (1,2,3,4), (2,4) ])
gap> Elements(D_8);
[ (), (2,4), (1,2)(3,4), (1,2,3,4), (1,3), (1,3)(2,4), (1,4,3,2), (1,4)(2,3) ]

You can find further information about IsPermGroup here