The leptonic sector in a recently proposed minimal extension of thestandard model, in which the permutation symmetry S_3 is assumed to be an exact flavor symmetry at the weak scale, is revisited. We find that S_3 with an additional Z_N symmetry allows one CP violating phase phi_nu in the neutrino mixing. The leptonic sector contains six real parameters besides the phase phi_nu to describe charged lepton and neutrino masses and the neutrino mixing. The model predicts: an inverted spectrum of neutrino mass, the absence of CP violating Dirac phase, tan theta_{23}=1+O(m_e^2/m_mu^2) and sin theta_{13}=0.0034+O(m_em_mu/m_{tau}^2). Neutrino mass as well as the effective Majorana mass m_ee in the neutrinoless double-$\beta$ decay can be expressed in a closed form as a function of phi_nu, Delta m^2_{21},Delta m^2_{23} and tan theta_{12}. The model also predicts m_ee > (0.036 - 0.066) eV.
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