  We analyze a classically scale invariant extension of the Standard Model with
dark gauge $U(1)_X$ broken by doubly charge scalar $\Phi$ leaving a remnant
$Z_2$ symmetry. Dark fermions are introduced as dark matter candidates and for
anomaly reasons we introduce two chiral fermions. Due to classical scale
invariance, bare mass term that would mix these two states is absent and they
end up as stable Majorana fermions $N_1$ and $N_2$. We calculate cross sections
for $N_aN_a \to \phi\phi$, $N_aN_a \to X^\mu \phi$ and $N_2N_2 \to N_1N_1$
annihilation channels. We put constraints to the model from the Higgs searches
at the LHC, dark matter relic abundance and dark matter direct detection limits
by LUX. The dark gauge boson plays a crucial role in the Coleman-Weinberg
mechanism and has to be heavier then 680 GeV. The viable mass region for dark
matter is from 470 GeV up to a few TeV. In the case when two Majorana fermions
have different masses, two dark matter signals at direct detection experiments
could provide a distinctive signature of this model.
