# Irreducible representations of finite lamplighter group

Let $G = \mathbb{Z}_2 \wr \mathbb{Z}_n$ be the finite lamplighter group. What are the irreducible representations of $G$ - can anyone provide a clear reference?

Austin, Naor and Valette list representations of $G$ here: http://arxiv.org/abs/0705.4662 (page 4), however, it seems to me that they are not all irreducible (dimension count gives $\sum_{\rho} d_{\rho}^2> |G|$).