  Assuming that the lepton, quark and Higgs fields belong to the
three-dimensional reducible representation of the permutation group S_3, we
suggest a minimal S_3 invariant extension of the standard model. We find that
in the leptonic sector, the exact S_3 x Z_2 symmetry, which allows 6 real
independent parameters with two CP-violating phases, is consistent with
experimental data and predicts a maximal mixing of the atmospheric neutrinos,
and that the third neutrino is the lightest neutrino. With the exact S_3 only,
there are 10 real parameters and five phases in the quark sector.
  A set of values of these parameters that are consistent with experimental
observations is given.
