  We present the first multiscalar singlet extension of the 3-3-1 model with
right-handed neutrinos, based on the $\Delta \left( 27\right) $ family
symmetry, supplemented by the $Z_{4}\otimes Z_{8}\otimes Z_{14}$ flavor group,
consistent with current low energy fermion flavor data. In the model under
consideration, the light active neutrino masses are generated from a double
seesaw mechanism and the observed pattern of charged fermion masses and quark
mixing angles is caused by the breaking of the $\Delta \left( 27\right) \otimes
Z_{4}\otimes Z_{8}\otimes Z_{14}$ discrete group at very high energy. Our model
has only 14 effective free parameters, which are fitted to reproduce the
experimental values of the 18 physical observables in the quark and lepton
sectors. The obtained physical observables for the quark sector agree with
their experimental values, whereas those ones for the lepton sector also do,
only for the inverted neutrino mass hierarchy. The normal neutrino mass
hierarchy scenario of the model is disfavored by the neutrino oscillation
experimental data. We find an effective Majorana neutrino mass parameter of
neutrinoless double beta decay of $m_{\beta \beta }=$ 22 meV, a leptonic Dirac
CP violating phase of $34^{\circ }$ and a Jarlskog invariant of about $10^{-2}$
for the inverted neutrino mass spectrum.
