2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/38515We generalize the concept of cubic group into any dimension and derive their conjugate classifications and representation theorys. Double group and spinor representation are defined. A detailed calculation is carried out on the structures of four-dimensional cubic group $O_4$ and its double group, as well as all inequivalent single-valued representations and spinor representations of $O_4$ . All representations are derived adopting Clifford theory of decomposition of induced representations.High Energy Physics - Latticetext