# Dimension of irreducible representations of finite p-groups

Let $G$ be a finite $p$-group. Is it true that every irreducible representation of $G$ over an algebraically closed field of characteristic zero ($\mathbb{C}$, for example) must have dimension a power of $p$?

Proof or reference are appreciated.

-

@Mariano & Jiangwe: In fact, it's even better: the square of the degree of each irreducible character of any finite nilpotent group $G$ divides $[G:Z(G)]$! –  Geoff Robinson Jul 13 '11 at 16:28