Calculating the Fundamental Group of Galois Cover of the(2, 3)-embedding of CP~1× T

As known to all,it is quite difficult to compute the fundamental group of a surface of general type.In this paper,applying Moishezon-Teicher's algorithm,we investigate the fundamental group of a special surface of general type with zero topological index,namely,the Galois cover of the(2,3)-embedding of CP~1×T.Because the full presentation of the group is very complicated,we compute its special quotient and get an interesting result about its structure.