Group of Frattini class two

Definition

For a group of prime power order

A group of prime power order is termed a group of Frattini class two if it is a Frattini-in-center group and the Frattini subgroup is elementary abelian, i.e., it is a group of Frattini length two.

Relation with other properties

Stronger properties

• Special group
• Extraspecial group

Weaker properties

• Frattini-in-center group
• Group of nilpotency class two
• Group of Frattini length two