7.75 ConjugacyClassSubgroups

ConjugacyClassSubgroups( G, U )

ConjugacyClassSubgroups returns the conjugacy class of the subgroup U in the group G. Signals an error if U is not a subgroup of G. The conjugacy class is returned as a domain, so all set theoretic functions are applicable (see Domains).

    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), (3,4,5) ] )
    gap> C := ConjugacyClassSubgroups( s5, a5 );
    ConjugacyClassSubgroups( s5, Subgroup( s5, 
    [ (1,2,3), (2,3,4), (3,4,5) ] ) )
    gap> Size( C );
    1 

Another example of such domains is given in section ConjugacyClassesSubgroups.

ConjugacyClassSubgroups calls
G.operations.ConjugacyClassSubgroups( G, U ) and returns this value.

The default function called is GroupOps.ConjugacyClassSubgroups, which creates a conjugacy class record (see Subgroup Conjugacy Class Records) Set Functions for Subgroup Conjugacy Classes). Look in the index under ConjugacyClassSubgroups to see for which groups this function is overlaid.

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