EndomorphismImages( G )
This returns the lists of images of the generators under the
endomorphisms, using the data in G.endomorphismClasses. In this
example two trivial normal subgroups have been excluded. The
remaining normal subgroup of a4 is k4, with quotient c3 and a4
has 8 elements of order 3 with which to generate a c3, and hence 8
endomorphisms in this class.
gap> EndomorphismImages( a4 );
[ [ (2,3,4), (2,4,3) ], [ (2,4,3), (2,3,4) ], [ (1,2,4), (1,4,2) ],
[ (1,4,2), (1,2,4) ], [ (1,4,3), (1,3,4) ], [ (1,3,4), (1,4,3) ],
[ (1,3,2), (1,2,3) ], [ (1,2,3), (1,3,2) ] ]
GAP 3.4.4