  A dark sector with non-abelian gauge symmetry provides a sound framework to
justify stable dark matter (DM) candidates. We consider scalar fields charged
under a $SU(N)$ gauge group, and show that the centre of $SU(N)$, the discrete
subgroup $Z_N$ also known as $N$-ality, can ensure the stability of scalar DM
particles. We analyse in some details two minimal DM models of this class,
based on $SU(2)$ and $SU(3)$, respectively. These models have non-trivial
patterns of spontaneous symmetry breaking, leading to distinctive
phenomenological implications. For the $SU(2)$ model these include a specific
interplay of two DM states, with the same interactions but different masses,
and several complementary DM annihilation regimes, either within the dark
sector or through the Higgs portal. The $SU(3)$ model predicts dark radiation
made of a pair of dark photons with a unique gauge coupling, as well as regimes
where DM semi-annihilations become dominant and testable.
