  In this paper we study actions of finite groups on closed connected
aspherical manifolds. Under some assumptions on the outer automorphism group of
the fundamental group of a closed connected aspherical manifold $M$, we prove
that the homeomorphism group of $M$ is Jordan, we bound the discrete degree of
symmetry of $M$ and obtain a rigidity result, and we study the number of
stabilizers of finite group actions on $M$. Thereafter, we show that closed
connected aspherical locally homogeneous spaces $H\setminus G/\Gamma$ satisfy
the necessary hypothesis on the outer automorphism group of the fundamental
group.
