Special group

Definition
A group of prime power order is termed special if its center, derived subgroup and Frattini subgroup all coincide. It turns out that in this case, the center must be an elementary abelian group.

Sometimes, the term special also includes the case of elementary abelian groups. Under this definition, a group is special if it is either special in the above sense or it is elementary abelian.

Stronger properties

 * Extraspecial group

Weaker properties

 * Group of nilpotency class two
 * UL-equivalent group