A Riemann surface of genus g is called a Hurwitz surface if it has an automorphism group with the maximal order among all Riemann surfaces of a genus g. The corresponding automorphism group is called a Hurwitz group. We will take the group PSL(2,13), known to be Hurwitz, and construct a Riemann surface having this automorphism group. This Riemann surface will be realized as a projective variety in P(C¹⁴).