  We investigate a so-called 331 extension of the Standard Model gauge sector
which accommodates neutrino masses and where the lightest of the new neutral
fermions in the theory is a viable particle dark matter candidate. In this
model, processes mediated by the additional $Z^{\prime}$ gauge boson set both
the dark matter relic abundance and the scattering cross section off of nuclei.
We calculate with unprecedented accuracy the dark matter relic density,
including the important effect of coannihilation across the heavy fermion
sector, and show that indeed the candidate particle has the potential of having
the observed dark matter density. We find that the recent LUX results put very
stringent bounds on the mass of the extra gauge boson, $M_{Z^{\prime}} \gtrsim
2$~TeV, independently of the dark matter mass. We also comment on regime where
our bounds on the $Z^{\prime}$ mass may apply to generic 331-like models, and
on implications for LHC phenomenology.
