AutomorphismGroupElements( A )
A must be an automorphism record as returned by one of the automorphism routines or a list consisting of automorphisms of a p-group P.
In the first case a list of all elements of Aut(P) or Aut_n(P) is
returned, if A has been created by Automorphisms
or NormalizedAutomorphisms (see Automorphisms),
respectively, or a list of coset representatives of Aut(P) or Aut_n(P)
modulo Inn(P), if A has been created by OuterAutomorphisms
or NormalizedOuterAutomorphisms (see Automorphisms), respectively.
In the second case the list of all elements of the subgroup of Aut(P) generated by A is returned.
gap> g:= SolvableGroup( "Q8" );;
gap> outg:= OuterAutomorphisms( g );;
gap> AutomorphismGroupElements( outg );
[ GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ a, b, c ] ),
GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ b, a, c ] ),
GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ a*b, b, c ] ),
GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ a*b*c, a, c ] ),
GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ b, a*b, c ] ),
GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ a, a*b*c, c ] ) ]
gap> l:= [ outg.generators[2] ];
[ GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ a*b, b, c ] ) ]
gap> AutomorphismGroupElements( l );
[ GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ a, b, c ] ),
GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ a*b, b, c ] ),
GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ a*c, b, c ] ),
GroupHomomorphismByImages( Q8, Q8, [ a, b, c ], [ a*b*c, b, c ] ) ]
GAP 3.4.4