  We study properties of the Hirzebruch class of quotient singularities
$\mathbb{C}^n/G$, where $G$ is a finite matrix group. The main result states
that the Hirzebruch class coincides with the Molien series of $G$ under
suitable substitution of variables. The Hirzebruch class of a crepant
resolution can be described specializing the orbifold elliptic genus
constructed by Borisov and Libgober. It is equal to the combination of Molien
series of centralizers of elements of $G$. This is an incarnation of the McKay
correspondence. The results are illustrated with several examples, in
particular of 4-dimensional symplectic quotient singularities.
