SOCCERANE DERIVATIVES OF GIVEN SYMMETRIES

Symmetrical properties of soccerane and its derivatives are discussed in the light of subduction of coset representations (CRs). The 60 vertices of soccerane are equivalent and construct a single orbit governed by the CR, I(h)(/C(s)). This orbit is divided into several orbits in the respective derivative, where the mode of the division is controlled by the subduction. The number of derivatives with a given formula and a given subsymmetry is calculated in terms of unit subduced cycle indices, which are derived from the subduction.