Clebsch-Gordan coefficients of symmetry groups

A method is given for the determination of Clebsch-Gordan coefficients of finite groups. The Clebsch-Gordan coefficients may be arranged into vectors which are eigenvectors of certain projection matrices. It is shown how an appropriate set of orthonormal eigenvectors of these matrices may be obtained; this set gives then a unitary matrix of Clebsch-Gordan coefficients. The symmetry properties of these Clebsch-Gordan coefficients are studied with special emphasis on the crystallographic space groups.