We study homomorphisms from Out(F3β) to Out(F5β), and
GL(m,K) for m<7, where K is a field of characteristic other
than 2 or 3. We conclude that all K-linear representations of dimension at
most 6 of Out(F3β) factor through GL(3,Z), and that all
homomorphisms from Out(F3β) to Out(F5β) have finite
image.Comment: Final versio