The f2-particle coefficients of fractional parentage for the group chain SU(mn) ⊃ SU(m) x SU(n) or U(mn) ⊃ U(m) x U(n), with arbitrary m and n and with as many as possible symmetries, are tabulated for systems with up to six particles and for f2 equal up to three. All the coefficients are in the form of square roots of simple fractions. The algorithm for the CPF as well as the symmetries of the CFP are discussed. Contents:The Algorithm:The SU(mn) ⊃ SU(m) x SU(n) Coefficients of Fractional ParentageThe CG Coefficients of Permutation GroupsThe S(f) ⊃ S (f1) x S (f2) ISFThe Calculation Formula for the CFPThe Properties of the CFPThe Phase ConventionThe Evaluation of the CFPDiscussionAppendixThe Use of the TablesTablesReferences Readership: Physicists, chemists and mathematicians. Keywords:Fractional Parentage