# Degree of irreducible representation may be greater than order of derived subgroup

## Statement

It is possible to have a finite group $G$ and an irreducible linear representation $\varphi$ of $G$ over a splitting field in characteristic zero such that the degree of $\varphi$ is strictly greater than the order of the Derived subgroup (?) of $G$.

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

## Related facts

For more facts, see degrees of irreducible representations.

### Related facts about conjugacy class sizes

These facts are related to the conjugacy class size statistics of a finite group.

## Proof

### Example of extraspecial group

Consider an extraspecial group of order $p^5$ for any prime number $p$. The derived subgroup has order $p$. However, this group has a faithful irreducible representation of degree $p^2$.