Maximal class group

The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter

Definition

A maximal class group is a group of prime power order with the following special structure:

The group has nilpotence class $c$ , and order $p c + 1$ , where $p$ is a prime number
The quotient of the group by its commutator subgroup has order $p 2$
The upper central series and lower central series coincide, and all the successive quotients (except the top-most quotient) are of order $p$