53.16 ClassesNormalSubgroup

ClassesNormalSubgroup( G, N )

returns the list of positions of conjugacy classes of the group G that are contained in the normal subgroup N of G.

    gap> ccl:= ConjugacyClasses( S4 );
    [ ConjugacyClass( S4, IdAgWord ), ConjugacyClass( S4, d ), 
      ConjugacyClass( S4, b ), ConjugacyClass( S4, a ), 
      ConjugacyClass( S4, a*d ) ]
    gap> V4:= NormalClosure( S4, Subgroup( S4, [ S4.4 ] ) );
    Subgroup( S4, [ c, d ] )
    gap> ClassesNormalSubgroup( S4, V4 );
    [ 1, 2 ]