Dihedral families of quarks, leptons, and Higgs bosons

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\ - (eta) over bar, \V-ub\ - sin2 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 x 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.