  We perform a comprehensive analysis of several phenomenological aspects of
the renormalizable extension of the inert 3-3-1 model with sequentially
loop-generated SM fermion mass hierarchy. Special attention is paid to the
study of the constraints arising from the experimental data on the $\rho$
parameter, as well as those ones resulting from the charged lepton flavor
violating process $\mu\to e\gamma$ and dark matter. We also study the single
$Z'$ production via Drell-Yan mechanism at the LHC. We have found that $Z'$
gauge bosons heavier than about $4$ TeV comply with the experimental
constraints on the oblique $\rho$ parameter as well as with the collider
constraints. In addition, we have found that the constraint on the charged
lepton flavor violating decay $\mu\rightarrow e\gamma$ sets the sterile
neutrino masses to be lighter than about $1.12$ TeV. In addition the model
allows charged lepton flavor violating processes within reach of the
forthcoming experiments. The scalar potential and the gauge sector of the model
are analyzed and discussed in detail. Our model successfully accommodates the
observed Dark matter relic density.
