[GAP Forum] IsConjugatorIsomorphism for A5

[Andreas Bächle]

Dear GAP-forum,

I encountered some (at least for me) unexpected behavior of the command 
IsConjugatorIsomorphism.

gap> G := SmallGroup(60,5);; StructureDescription(G);
"A5"
gap> S := SylowSubgroup(G, 2);
Group([ (2,4)(3,5), (2,3)(4,5) ])
gap> A := AutomorphismGroup(G);;
gap> f := AsList(A)[1];
^()
gap> g := RestrictedMapping(f, S);
GeneralRestrictedMapping( ^(), Group([ (2,4)(3,5), (2,3)(4,5) ]), A5 )
gap> IsConjugatorIsomorphism(g);
false

When I run this with other groups from the SmallGroup library everything 
seems to work and I get the expected output "true".

My first guess was that G (or S) is / are of a data type conflicting 
with the natural embedding described in 
http://www.gap-system.org/Manuals/doc/ref/chap40.html#X7F31FECC7A3D4A8A  
However

gap> IsPermGroup(G);
true
gap> IsPermGroup(S);
true

When replacing G by an isomorphic fp-group (H := 
Image(IsomorphismFpGroup(G));) it works (but is quite slow).  Also with 
other simple / perfect groups the result is as expected.  What is so 
special about this case?  And is there a good workaround to make this 
work for all groups from the SmallGroup library?

Thanks in advance for any help,
   Andreas Bächle