The fusion algebra of an extraspecial p-group

One can remark that the study of twisted fusion algebras for finite groups is closely related to the modular data associated with finite groups. Coste ["Finite group modular data," Nucl. Phys. B, 521, 679] undergo the study of this finite group modular data and write down the modular S and T matrices of the group G= (Z/p)3 for a particular twist. Here we show that the modular data of G for a particular twist are the same as the modular data of the extraspecial p -group H of order p₃ with exponent p. This result implies that the twisted fusion algebra of G is the same as the nontwisted fusion algebra of H.