On irreducible corepresentations of finite magnetic groups

We have obtained a set of homogeneous linear equations in the Clebsch-Gordan coefficients for the Kronecker inner direct product of two irreducible corepresentations of a finite magnetic group. The solutions of these equations give the Clebsch-Gordan coefficients even when the group is not simply reducible. The nontrivial Clebsch-Gordan coefficients for the magnetic group C4ν(C2ν) have been evaluated. We have also investigated the criterion determining whether a particular irreducible corepresentation is equivalent to its complex conjugate representation. A projection operator has been constructed for obtaining the basis pertaining to a particular irreducible corepresentation.