We consider a scale invariant extension of the standard model (SM) with a combined breaking of conformal and electroweak symmetry in a strongly interacting hidden $SU(n_c)$ gauge sector with $n_f$ vector-like hidden fermions. The (pseudo) Nambu-Goldstone bosons that arise due to dynamical chiral symmetry breaking are dark matter (DM) candidates. We focus on $n_f=n_c=3$, where $SU(3)$ is the largest symmetry group of hidden flavor which can be explicitly broken into either $U(1) times U(1)$ or $SU(2)times U(1)$. We study DM properties and discuss consistent parameter space for each case. Because of different mechanisms of DM annihilation the consistent parameter space in the case of $SU(2)times U(1)$ is significantly different from that of $SU(3)$ if the hidden fermions have a SM $U(1)_Y$ charge of $O(1)$.
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