  We study the mod-p cohomology of the group Out(F_n) of outer automorphisms of
the free group F_n in the case n=2(p-1) which is the smallest n for which the
p-rank of this group is 2. For p=3 we give a complete computation, at least
above the virtual cohomological dimension of Out(F_4) (which is 5). More
precisley, we calculate the equivariant cohomology of the p-singular part of
outer space for p=3. For a general prime p>3 we give a recursive description in
terms of the mod-p cohomology of Aut(F_k) for k less or equal to p-1. In this
case we use the Out(F_{2(p-1)})-equivariant cohomology of the poset of
elementary abelian p-subgroups of Out(F_n).
