Given a finite group G, denote by D(G) the degree pattern of G and by OC(G) the set of all order components of G. Denote by hOD(G) (resp. hOC(G)) the number of isomorphism classes of finite groups H satisfying conditions |H| = |G| and D(H) = D(G) (resp. OC(H) = OC(G)). A finite group G is called OD-characterizable (resp. OC-characterizable) if hOD(G) = 1 (resp. hOC(G) = 1). Let C = Cp(2) be a symplectic group over the binary field, for which 2p − 1 > 7 is a Mersenne prime. The aim of this article is to prove that hOD(C) = 1 = hOC(C).