  We use the eigenfunction method to calculate the Clebsh-Gordan coefficients
for the permutation group . This method is well-established by Jin-Quan Chen.
Here we elaborate the detailed procedures for the pedagogical purpose. Due to
the nature of the symmetry, one may get the degeneracy from the solution of
eigenfunctions for given one class operator. In order to remove the degeneracy
we use extra class operators, which may be the subgroup class operator or even
the state permutation operator. In doing so, a variety of eigenvalues come out.
Every eigenfunction is therefore obtained, and basis vectors are completely
found.
