  We examine the Johnson filtration of the (outer) automorphism group of a
finitely generated group. In the case of a free group, we find a surprising
result: the first Betti number of the second subgroup in the Johnson filtration
is finite. Moreover, the corresponding Alexander invariant is a non-trivial
module over the Laurent polynomial ring. In the process, we show that the first
resonance variety of the outer Torelli group of a free group is trivial. We
also establish a general relationship between the Alexander invariant and its
infinitesimal counterpart.
