We give explicit formulas for the structure coefficients of the center of the symmetric group algebra involving the class of two transpositions. In particular, we show the explicit expression for the product of the class of two transpositions with the class of cycles of a given length k. In addition a formula for the structure coefficient  for any partition λ of n is given.

The center of the symmetric group algebra, structure coefficients, product of conjugacy classes of the symmetric group, representation theory of the symmetric group.