The algebra of coupling and recoupling coefficients relative to a (finite) subgroup G of the special unitary group in two dimensions SU (2) is developed in this paper. Following the work of Schönfeld on the cubic field, and the work of Flato on the trigonal and tetragonal fields, the f symbols are defined from the Clebsch-Gordan coefficients ( j 1 j 2 m 1 m 2 ∥ j 1 j 2 j 3 m 3) expressed in the jΓ γ scheme where Γ γ stands for the γ-row of the irreducible representation Γ of G. The definition of the irreducible tensorial sets under the group G, leads to the Wigner-Eckart theorem. Properties of the f coefficients and of the related f are obtained from the properties of the 3 - j Wigner's symbols for SU (2). Utilizing the technique developed by Racah, the recoupling coefficients W and X are calculated as function of f . Numerical values of the f's for the cubic and tetragonal groups (electronic configurations d 2, f 2) are given in the appendix.