We introduce the flavor symmetry ${bf Z}_M times {bf Z}_N times D_4$ into the $SU(6) times SU(2)_R$ string-inspired model. The cyclic group ${bf Z}_M$ and the dihedral group $D_4$ are R symmetries, while ${bf Z}_N$ is a non-R symmetry. By imposing the anomaly-free conditions on the model, we obtain a viable solution under many phenomenological constraints coming from the particle spectra. For neutrino sector, we find a LMA-MSW solution but not SMA-MSW ones. The solution includes phenomenologically acceptable results concerning fermion masses and mixings and also concerning hierarchical energy scales including the GUT scale, the $mu$ scale and the Majorana mass scale of R-handed neutrinos.
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