The flavor group Δ(6n2)

Many non-Abelian finite subgroups of SU(3) have been used to explain the flavor structure of the standard model. In order to systematize and classify successful models, a detailed knowledge of their mathematical structure is necessary. In this paper, we shall therefore look closely at the series of finite non-Abelian groups known as Δ(6n2), its smallest members being S3 (n=1) and S4 (n=2). For arbitrary n, we determine the conjugacy classes, the irreducible representations, the Kronecker products, as well as the Clebsch–Gordan coefficients.