7.82 ConjugateSubgroups

ConjugateSubgroups( G, U )

ConjugateSubgroups returns the orbit of U under G acting by conjugation (see ConjugateSubgroup) as list of subgroups. U and G must have a common parent group.

    gap> s4 := Group( (1,2,3,4), (1,2) );
    Group( (1,2,3,4), (1,2) )
    gap> s3 := Subgroup( s4, [ (1,2,3), (1,2) ] );
    Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,2,3), (1,2) ] )
    gap> ConjugateSubgroups( s4, s3 );
    [ Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,2,3), (1,2) ] ), 
      Subgroup( Group( (1,2,3,4), (1,2) ), [ (2,3,4), (2,3) ] ), 
      Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,3,4), (3,4) ] ), 
      Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,2,4), (1,4) ] ) ] 

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