Materials that crystallize in diamond-related lattices, with Si and GaAs as their prime examples, are at the foundation of modern electronics. Simultaneously, inversion asymmetries in their crystal structure and relativistic spin–orbit coupling led to discoveries of non-equilibrium spin-polarization phenomena that are now extensively explored as an electrical means for manipulating magnetic moments in a variety of spintronic structures. Current research of these relativistic spin–orbit torques focuses primarily on magnetic transition-metal multilayers. The low-temperature diluted magnetic semiconductor (Ga, Mn)As, in which spin–orbit torques were initially discovered, has so far remained the only example showing the phenomenon among bulk non-centrosymmetric ferromagnets. Here we present a general framework, based on the complete set of crystallographic point groups, for identifying the potential presence and symmetry of spin–orbit torques in non-centrosymmetric crystals. Among the candidate room-temperature ferromagnets we chose to use NiMnSb, which is a member of the broad family of magnetic Heusler compounds. By performing all-electrical ferromagnetic resonance measurements in single-crystal epilayers of NiMnSb we detect room-temperature spin–orbit torques generated by effective fields of the expected symmetry and of a magnitude consistent with our ab initio calculations.