Abstract. In this paper, for a possibly singular complex variety X, generating functions of total orbifold Chern homology classes of the symmetric products S n X are given. Those are very natural "class versions" of known generating function formulae of (generalized) orbifold Euler characteristics of S n X. The classes work covariantly for proper morphisms. We state the result more generally. Let G be a finite group and Gn the wreath product G ∼ Sn. For a G-variety X and a group A, we give a"Dey-Wohlfahrt type formula" for equivariant Chern-SchwartzMacPherson classes associated to Gn-representations of A (Theorem 1.1 and 1.2). In particular, if X is a point, this recovers a known exponential formula for counting numbers |Hom(A, Gn)|.