  The decay tau- -> 2pi- pi+ 3pi0 nu_tau has been studied with the CLEO II
detector at the Cornell Electron Storage Ring (CESR). The branching fraction is
measured to be (2.85 +/- 0.56 +/- 0.51) x 10^(-4). The result is in good
agreement with the isospin expectation but somewhat below the
Conserved-Vector-Current (CVC) prediction. We have searched for resonance
substructure in the decay. Within the statistical precision, the decay is
saturated by the channels tau- -> pi- 2pi0 omega nu_tau, 2pi- pi+ eta nu_tau,
and pi- 2pi0 eta nu_tau. This is the first observation of this omega decay mode
and the branching fraction is measured to be (1.89 +0.74/-0.67 +/- 0.40) x
10^(-4).
