In a model with an extra $U\left(1\right)$ gauge to SM gauge group, we have shown the allowed region of masses of the extra gauge boson and the dark matter which is the lightest one among other right-handed Majorana fermions present in the model. To obtain this region, we have used bounds coming from constraints on active-sterile neutrino masses and mixing from various oscillation experiments, constraint on dark matter relic density obtained by PLANCK together with the constraint on the extra gauge boson mass and its gauge coupling recently obtained by ATLAS Collaboration at LHC. From the allowed regions, it is possible to get some lower bounds on the masses of the extra gauge boson and the dark matter and considering those values it is possible to infer what could be the spontaneous symmetry breaking scale of an extra $U\left(1\right)$ gauge symmetry.