Realizing regular representations of finite groups

Given a regular representation of a finite group G and a positive integer number n , we construct a (finite) topological space X such that its group of homotopy classes of self-homotopy equivalences E ( X ) and its group of homeomorphisms A u t ( X ) are isomorphic to G , and the action of G on the n -th homology group H n ( X ) is the regular representation. We also discuss other representations.