7.80 MaximalSubgroups

MaximalSubgroups( G )

MaximalSubgroups calculates all maximal subroups of the special ag group G.

    gap> s4 := SymmetricGroup( AgWords, 4 );;
    gap> ss4 := SpecialAgGroup( s4 );;
    gap> MaximalSubgroups( ss4 );
    [ Subgroup( Group( g1, g2, g3, g4 ), [ g2, g3, g4 ] ), 
      Subgroup( Group( g1, g2, g3, g4 ), [ g1, g3, g4 ] ), 
      Subgroup( Group( g1, g2, g3, g4 ), [ g1*g2^2, g3, g4 ] ), 
      Subgroup( Group( g1, g2, g3, g4 ), [ g1*g2, g3, g4 ] ), 
      Subgroup( Group( g1, g2, g3, g4 ), [ g1, g2 ] ), 
      Subgroup( Group( g1, g2, g3, g4 ), [ g1, g2*g3*g4 ] ), 
      Subgroup( Group( g1, g2, g3, g4 ), [ g1*g4, g2*g4 ] ), 
      Subgroup( Group( g1, g2, g3, g4 ), [ g1*g4, g2*g3 ] ) ]  

ConjugacyClassesMaximalSubgroups (see ConjugacyClassesMaximalSubgroups) computes the list of conjugacy classes of maximal subgroups.

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