  Let $G$ be a finite group, $A$ a finite abelian group. Each homomorphism
$\phi:G\to A\wr S_n$ induces a homomorphism $\bar{\phi}:G\to A$ in a natural
way. We show that as $\phi$ is chosen randomly, then the distribution of
$\bar{\phi}$ is close to uniform. As application we prove a conjecture of T.
M\"uller on the number of homomorphisms from a finite group into Weyl groups of
type $D_n$.
