In a previous paper, many nucleon states in the shell model are characterized through the group C2 used for an exact treatment of charge independent pairing interaction. This scheme was proved to be equivalent to Flowers' seniority-reduced-isospin scheme. The matrix elements of pair creation operator (a generator of the group C2) are connected with the coefficients of fractional parentage of the type which play an essential role in seniority scheme. Then a simple method of calculation of the matrix elements of pair operator is developed, and they are tabulated up to λ1+λ2≤4 (complete for up to f7/2 shell). A recursion formula of c.f.p. in seniority scheme is derived, which is more general than that of de-Shalit and Talmi.