7.79 ConjugacyClassesMaximalSubgroups

ConjugacyClassesMaximalSubgroups( G )

ConjugacyClassesMaximalSubgroups returns a list of conjugacy classes of maximal subgroups of the group G.

A subgroup H of G is maximal if H is a proper subgroup and for all subgroups I of G with H < I leq G the equality I = G holds.

    gap> s4 := SymmetricGroup( AgWords, 4 );;
    gap> ss4 := SpecialAgGroup( s4 );;
    gap> ConjugacyClassesMaximalSubgroups( ss4 );
    [ ConjugacyClassSubgroups( Group( g1, g2, g3, g4 ), Subgroup( Group(
        g1, g2, g3, g4 ), [ g2, g3, g4 ] ) ),
      ConjugacyClassSubgroups( Group( g1, g2, g3, g4 ), Subgroup( Group(
        g1, g2, g3, g4 ), [ g1, g3, g4 ] ) ),
      ConjugacyClassSubgroups( Group( g1, g2, g3, g4 ), Subgroup( Group(
        g1, g2, g3, g4 ), [ g1, g2 ] ) ) ]

The generic method computes the entire lattice of conjugacy classes of subgroups (see Lattice) and returns the maximal ones.

MaximalSubgroups (see MaximalSubgroups) computes the list of all maximal subgroups.

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