In this paper, we investigate the problem of a size-constrained k-core group query (SCCGQ) in social networks, taking both user closeness and network topology into consideration. More specifically, SCCGQ intends to find a group of h users that has the highest social closeness while being a k-core. SCCGQ can be widely applied to event planning, task assignment, social analysis, and many other fields. In contrast to existing work on the k-core detection problem, which aims to find a k-core in a social network, SCCGQ not only focuses on k-core detection but also takes size constraints into consideration. Although the conventional k-core detection problem can be solved in linear time, SCCGQ has a higher complexity. To solve the problem of SCCGQ, we propose a Blast Scatter (BS) algorithm, which appoints the query node as the center to begin outward expansions via breadth search. In each outward expansion, BS finds a new center through a greedy strategy and then selects multiple neighbors of the center. To speed up the BS algorithm, we propose an advanced search algorithm, called Bounded Extension (BE). Specifically, BE combines an effective social distance pruning strategy and a tight upper bound of social closeness to prune the search space considerably. In addition, we propose an offline social-aware index to accelerate the query processing. Finally, our experimental results demonstrate the efficiency and effectiveness of our proposed algorithms on large real-world social networks.