Semigroups of finite ramified coverings of Riemannian surfaces

A semigroup structure will be defined on the equivalence classes of d-sheeted ramified marked coverings of Riemannian surfaces with fixed Galois group. As application, I give conditions on the Galois group of coverings and the ramification type that allow to reconstruct the covering uniquely by means of its ramification type, and in general case, an answer on the question about the number of non-equivalent coverings of fixed type will be given if the number of branch points is big enough.