Permutational symmetry of Clebsch-Gordan coefficients for the metacyclic groups

A complete discussion of the permutational symmetry for the 3Gcy] γ-symbols for K-metacyclic groups, an example of non-simple-phase groups, is carried out. The analytic formulas for the 3Gcy] γ-symbols, and for the Derome-Sharp matrices, describing the permutational properties of these symbols are given. It is shown that these matrices constitute a permutation representation m, which is an appropriate “coarse-grained” version of the ordinary permutation representation of the group of all permutations of columns of the 3Gcyγ symbols. A detailed structure of the representation m has been determined.