  We consider finite group-actions on 3-manifolds $\cal H_g$ obtained as the
connected sum of $g$ copies of $S^2 \times S^1$, with free fundamental group
$F_g$ of rank $g$. We prove that, for $g > 1$, a finite group of
diffeomorphisms of $\cal H_g$ inducing a trivial action on homology is cyclic.
As a consequence, no non-cyclic subgroup of the twist subgroup of the mapping
class group of $\cal H_g$ (generated by Dehn twists along embedded 2-spheres)
can be realized by diffeomorphisms (in the sense of the Nielsen realization
problem). We also discuss when a finite subgroup of the outer automorphism
group ${\rm Out}(F_g)$ of the fundamental group of $\cal H_g$ can be realized
by a group of diffeomorphisms of $\cal H_g$.
