[GAP Forum] finding all isomorphisms

[Marc Roeder]

Hi Bob,

here's one way of getting all isomorphisms:
Get one isomorphism and the group of automorphisms and then take all
compositions.

Example:
gap> G:=Group([(1,2),(3,4)]);
Group([ (1,2), (3,4) ])
gap> iso:=IsomorphismGroups(G,SmallGroup(4,2));
[ (1,2), (3,4) ] -> [ f1, f2 ]
gap> allisos:=List(AutomorphismGroup(G),alpha->alpha*iso);
[ [ (1,2), (3,4) ] -> [ f1, f2 ], [ (1,2), (3,4) ] -> [ f1*f2, f2 ],
  [ (1,2), (3,4) ] -> [ f2, f1 ], [ (1,2), (3,4) ] -> [ f1*f2, f1 ],
  [ (1,2), (3,4) ] -> [ f2, f1*f2 ], [ (1,2), (3,4) ] -> [ f1, f1*f2 ] ]


Hope that helps,
marc