Dihedral Groups of order $2p$ of Automorphisms of Compact Riemann Surfaces of Genus $p-1$ In this paper we prove that there is only one conjugacy class of dihedral group of order $2p$ in the $2(p-1)\times 2(p-1)$ integral symplectic group can be realized by an analytic automorphism group of compact connected Riemann surfaces of genus $p-1$. A pair of representative generators of the realizable class is also given. Keywords:dihedral group, automorphism group, Riemann surface, integral symplectic matrix, fundamental domainCategories:20H25, 57M60