Abstract
A general method is developed for obtaining Clebsch-Gordan coefficients of finite groups. With this method Clebsch-Gordan coefficients are obtained in a matrix form, whereas the so-called basis-function generating machine generates these coefficients one by one. The method is applied to double point group D̄3, the point group T, and the nonsymmorphic space group D̄4h14. It will be shown that the method can be simplified by the conservation law of the reduced wave vectors when applied to space groups.

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