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We propose a 3-3-1 model where the $SU(3)_{C}\otimes SU(3)_{L}\otimesU(1)_{X}$ symmetry is extended by $S_{3}\otimes Z_{3}\otimes Z_{3}^{\prime}\otimes Z_{8}\otimes Z_{16}$ and the scalar spectrum is enlarged by extra $%SU(3)_{L}$ singlet scalar fields. The model successfully describes the observedSM fermion mass and mixing pattern. In this framework, the light activeneutrino masses arise via an inverse seesaw mechanism and the observed chargedfermion mass and quark mixing hierarchy is a consequence of the $Z_{3}\otimesZ_{3}^{\prime }\otimes Z_{8}\otimes Z_{16}$ symmetry breaking at very highenergy. The obtained physical observables for both quark and lepton sectors arecompatible with their experimental values. The model predicts the effectiveMajorana neutrino mass parameter of neutrinoless double beta decay to be$m_{\beta \beta }=$ 4 and 48 meV for the normal and the inverted neutrinospectra, respectively. Furthermore, we found a leptonic Dirac CP violatingphase close to $\frac{\pi }{2}$ and a Jarlskog invariant close to about$3\times 10^{-2}$ for both normal and inverted neutrino mass hierarchy.

Fermion masses and mixings in the 3-3-1 model with right-handed neutrinos based on the $S_3$ flavor symmetry