  Hodge classes on the moduli space of admissible covers with monodromy group G
are associated to irreducible representations of G. We evaluate all linear
Hodge integrals over moduli spaces of admissible covers with abelian monodromy
in terms of multiplication in an associated wreath group algebra. In case G is
cyclic and the representation is faithful, the evaluation is in terms of double
Hurwitz numbers. In case G is trivial, the formula specializes to the
well-known result of Ekedahl-Lando-Shapiro-Vainshtein for linear Hodge
integrals over the moduli space of curves in terms of single Hurwitz numbers.
