# Nilpotency class and order determine group up to commutator map-equivalence for up to prime-fourth order

From Groupprops

This article gives a fact that is true forsmallgroups of prime power order.More specifically, it is true for all groups of order where is at most equal to 4.

See more such facts| See more facts true for prime powers up to the same maximum power 4

## Statement

Suppose and are natural numbers and . Suppose is a prime number. Then, if are groups both of order and nilpotency class *exactly* , and must be Commutator map-equivalent groups (?).