Isoscalar factors of the permutation group

We propose a phase convention for the Clebsch-Gordan coefficients of S_n and present tables of isoscalar factors for S_3,S_4,S_5 and S_6. The isoscalar factors have been calculated from a recursion relation due to Hamermesh and by using symmetry properties of the Clebsch-Gordan coefficients. Applications of the study of multiquark systems are discussed.