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A finite subgroup of ${\rm SL}_2(\CC)$ defines a (Kleinian) rational surfacesingularity. The McKay correspondence yields a relation between the Poincar\'eseries of the algebra of invariants of such a group and the characteristicpolynomials of certain Coxeter elements determined by the correspondingsingularity. Here we consider some non-abelian finite subgroups $G$ of ${\rmSL}_3(\CC)$. They define non-isolated three-dimensional Gorenstein quotientsingularities. We consider suitable hyperplane sections of such singularitieswhich are Kleinian or Fuchsian surface singularities. We show that we obtain asimilar relation between the group $G$ and the corresponding surfacesingularity.

A McKay correspondence for the Poincar\'e series of some finite subgroups of ${\rm SL}_3(\CC)$