7.24 FrattiniSubgroup

FrattiniSubgroup( G )

FrattiniSubgroup returns the Frattini subgroup of group G.

The Frattini subgroup of a group G is the intersection of all maximal subgroups of G.

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

The generic method computes the Frattini subgroup as intersection of the cores (see Core) of the representatives of the conjugacy classes of maximal subgroups (see ConjugacyClassesMaximalSubgroups).

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