7.76 IsConjugacyClassSubgroups

IsConjugacyClassSubgroups( obj )

IsConjugacyClassSubgroups returns true if obj is a conjugacy class of subgroups as created by ConjugacyClassSubgroups (see ConjugacyClassSubgroups) and false otherwise.

    gap> s5 := Group( (1,2), (1,2,3,4,5) );;  s5.name := "s5";;
    gap> a5 := DerivedSubgroup( s5 );
    Subgroup( s5, [ (1,2,3), (2,3,4), (2,4)(3,5) ] )
    gap> c := ConjugacyClassSubgroups( s5, a5 );
    ConjugacyClassSubgroups( s5, Subgroup( s5, 
    [ (1,2,3), (2,3,4), (2,4)(3,5) ] ) )
    gap> IsConjugacyClassSubgroups( c );
    true
    gap> IsConjugacyClassSubgroups( [ a5 ] );
    false    # even though this is as a set equal to 'c' 

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