For a given flat manifold M, we obtain a sufficient and necessary   condition for a finite group that could act effectively on M. Two applications will be discussed. The first is about topological Zimmer’s   program and the second is about Jordan’s property of homeomorphism groups. In   particular, we prove that any action of SL(n,Z) (n>2) on a flat manifold M is trivial   when dim(M)<n. This confirms a conjecture related to Zimmer's program for   flat manifolds.