  We consider finite groups of small order for family symmetry. It is found
that the binary dihedral group Q_6, along with the assumption that the Higgs
sector is of type II, predicts mass matrix of a nearest neighbor interaction
type for quarks and leptons. We present a supersymmetric model based on Q_6
with spontaneously induced CP phases. The quark sector contains 8 real
parameters with one independent phase to describe the quark masses and their
mixing. Predictions in the |V_{ub}|-bar{eta}, |V_{ub}|-sin 2 beta(phi_1) and
|V_{ub}|-|V_{td}/V_{ts}| planes are given. The lepton sector contains also 9
parameters. A normal as well as an inverted spectrum of neutrino masses is
possible, and we compute V_{e3}. We find that |V_{e3}|^2 > 10^{-4} in the case
of a normal spectrum, and |V_{e3}|^2 >8 10^{-4} in the case of an inverted
spectrum. It is also found that Q_6 symmetry forbids all Baryon number
violating terms of d=4, and the contributions to EDMs from the A terms vanish
in this model.
