Factorization of the noncommutative permutation matrices with not prime order

The present results concern the explicit factorization of the noncommutative permutation matrices with not prime order on the closed Riemann surface R with genus r. The given problem is solved by means of the effective factorization of the corresponding commutative permutation matrix with the less order than the initial one, and such matrix is considered on the closed Riemann surface whose genus is bigger than r.