We consider the coded caching problem with a central server containing N files, each of length F bits, and K users, each equipped with a cache of capacity MF bits. We assume that coded contents can be proactively placed into users' caches at no cost during the placement phase. During the delivery phase, each user requests exactly one file from the database, and all the requests are served simultaneously by the server over an error-free common link. The goal is to utilize the local cache memories at the users to reduce the delivery rate from the server during the peak period. Here, we focus on a system which has more users than files, i.e., K > N. We first consider the centralized caching problem, in which the number and identity of active users are known in advance, and propose a group-based coded caching scheme for M = N/K, which improves upon the best achievable scheme in the literature. The proposed centralized caching scheme is then exploited in a decentralized setting, in which neither the number nor the identity of the active users are known during the placement phase. It is shown that the proposed coded caching scheme improves upon the best known decentralized delivery rate as well.