[GAP Forum] RepresentativeAction gives error

[Andrew Johnson]

I'm using GAP (gap4r4p6-win.zip) to investigate some permutation groups.

group1 := Group([ (1,3)(2,5)(4,7)(6,8), (1,4)(2,6)(3,7)(5,8),
(1,5)(2,3)(4,8)(6,7),
  (2,3,4,5,7,8,6), (3,4,7)(5,6,8) ]);
group2 := Group([ (1,3,4,7,2,6,8), (1,8,7,5,3,6,2) ]);
group3 := SymmetricGroup([1..8]);

RepresentativeAction(group3,group1,group2);

gives:
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 1st choice method found for `ONE' on 1 arguments called from
OneOp( elm ) called from
One( F ) called from
CallFuncList( Refinements.(Rf.func), Concatenation( [ rbase, image ],
Rf.args
   ) ) called from
RRefine( rbase, image, false ) called from
PBEnumerate( 1, not repr ) called from
...
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

Is this expected?

My work around is to use
First(AsList(group3),e->group1^e=group2);

If this gets too slow, then I might use
IsomorphismGroups(group1, group2)
to see first of all whether the groups are isomorphic

or compare cycle structures of the elements.

signature2:= function(g)
local cg,c2;
cg := ConjugacyClasses(g);
c2 := List(cg, c->[CycleStructurePerm(Representative(c)),Size(c)]);
return SortedList(c2);
end;

to weed out groups which are clearly not conjugate.

[The reference manual for IsConjugate says 'This command is only a shortcut
to RepresentativeOperation.' I presume this should be updated to the
prefered name of RepresentativeAction.]

Andrew Johnson