# Degree of irreducible projective representation divides order of group

From Groupprops

## Contents

## Statement

Suppose is a finite group, is an algebraically closed field whose characteristic does not divide the order of , and is an irreducible projective representation of over of degree . Then, divides the order of .

This gives a numerical constraint on the degrees of irreducible projective representations.

## Related facts

### Stronger facts

- Degree of irreducible projective representation divides index of cyclic normal subgroup
- Degree of irreducible projective representation divides index of abelian normal subgroup to which its cohomology class restricts trivially