Problems with symmetric groupos

[enriqu...@gmail.com]

The following code gives problems:

sage: A5 = AlternatingGroup(5)
sage: h0 = A5.hom(codomain=A5, im_gens=A5.gens())
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [22], line 1
----> 1 h0 = A5.hom(codomain=A5, im_gens=A5.gens())

...

libgap.function_factory("GroupHomomorphismByImagesNC")

ValueError: images do not define a group homomorphism

It is probably related with the following:

sage: A5.gens()
((3,4,5), (1,2,3,4,5))
sage: libgap(A5).GeneratorsOfGroup()
[ (1,2,3,4,5), (3,4,5) ]

I works for AlternatingGroup(n) for n = 3, 4.

Probably independent problem, but if I want to construct a presentation of a group after importing wrap_FpGroup the code wrap_FpGroup(libgap(G).IsomorphismFpGroup().Range()) works for 

PermutationGroup([(1,2),(1,2,3,4)]) but not for SymmetricGroup(4)

Thanks, Enrique.