73.135 EndomorphismImages

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) ] ]  

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GAP 3.4.4
April 1997