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

Algebraic Geometry;Representation Theory