Frattini subgroup

In group theory, the Frattini subgroup is the intersection of all maximal subgroups of a group.

Formally,


 * $$\Phi(G) = G \cap \bigcap_M M \,$$

where M runs over all maximal subgroups of G. If G has no maximal subgroups then $$\Phi(G) = G$$.

The Frattini is a subgroup, which is normal and indeed characteristic.