  We obtain a sufficient and necessary condition for a finite group to act
effectively on a closed flat manifold. Let \ $G=E_{n}(R)$, $EU_{n}(R,\Lambda
),$ $\mathrm{SAut}(F_{n})$ or $\mathrm{SOut}(F_{n}).$ As applications, we prove
that when $n\geq 3$ every group action of $G$ on a closed flat manifold $M^{k}$
($k<n$) by homeomorphisms is trivial. This confirms a conjecture related to
Zimmer's program for flat manifolds. Moreover, it is also proved that the group
of homeomorphisms of closed flat manifolds are Jordan with Jordan constants
depending only on dimensions.
