Finite Group Databasebeta

Frattini subgroup

The Frattini subgroup Φ(G) is the intersection of all maximal subgroups of G (and G itself when there are none). Its elements are the "non-generators"; for a finite p-group Φ(G) = Gp [G, G], and G / Φ(G) is the largest elementary abelian quotient.

Wikipedia: Frattini subgroup