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