We perform a comprehensive analysis of several phenomenological aspects of the renormalizable extension of the inert 3-3-1 model with sequentially loop-generated Standard Model 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 -> 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 -> 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.