Summary: The middle homology of the Milnor fiber of a quasihomogeneous polynomial with an isolated singularity is a \(Z\)-lattice and comes equipped with an automorphism of finite order, the integral monodromy. P. Orlik [Lect. Notes Math. 298, 260–269 (1972; Zbl 0249.57029)] made a precise conjecture, which would determine this monodromy in terms of the weights of the polynomial. Here we prove this conjecture for the cycle type singularities. A paper of B. G. Cooper [Trans. Am. Math. Soc. 269, 149–166 (1982; Zbl 0487.14001)] with the same aim contained two mistakes. Still it is very useful. We build on it and correct the mistakes. We give additional algebraic and combinatorial results.