Clebsch-Gordan decomposition for transitive representations

The method of evaluation of Clebsch–Gordan coefficients to calculate the direct product of transitive representations for a finite group is developed. This procedure is based on the Mackey theorem and on the canonical realization of transitive representations. It is shown that the Clebsch–Gordan decomposition is associated with a natural interpretation of an orbit of a resultant transitive representation and it is analogous to a fibre bundle with the fibration being determined by constituent transitive representations.