# All partial sum values of squares of degrees of irreducible representations 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

## Contents

## 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 partial sum values of squares of degrees of irreducible representations divide the order of the group.

In this case, it means that for any , the sum of squares of degrees of irreducible representations of that are at most is itself a power of .

## Related facts

### Opposite facts

### Related facts for conjugacy class sizes

- All cumulative conjugacy class size statistics values divide the order of the group for groups up to prime-fifth order
- There exist groups of prime-sixth order in which the cumulative conjugacy class size statistics values do not divide the order of the group