Homomorphisms from a finite group into wreath products

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

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