# All cumulative conjugacy class size statistics values divide the order of the group for groups up to prime-fifth 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 5.

See more such facts| See more facts true for prime powers up to the same maximum power 5

## Statement

Suppose is a prime number and is an integer satisfying . Suppose is a group of order . Then, is a finite group in which all cumulative conjugacy class size statistics values divide the order of the group.

In this case, it means that for any , the number of elements of whose conjugacy class has size dividing is itself a power of .