# Degree of irreducible projective representation divides index of cyclic normal subgroup

## Statement

Suppose $G$ is a finite group, $H$ is a Cyclic normal subgroup (?) of $G$, and $K$ is an algebraically closed field whose characteristic does not divide the order of $G$. Suppose that $\varphi$ is an irreducible projective representation of $G$ over $K$.

Then, the degree of $\varphi$ divides the index of $H$ in $G$.

This is a numerical constraint on the Degrees of irreducible projective representations (?).

## Proof

The proof follows directly from Facts (1) and (2).