Automorphism groups of finite posets

For any finite group G , we construct a finite poset (or equivalently, a finite T 0 -space) X , whose group of automorphisms is isomorphic to G . If the order of the group is n and it has r generators, X has n ( r + 2 ) points. This construction improves previous results by G. Birkhoff and M.C. Thornton. The relationship between automorphisms and homotopy types is also analyzed.