With the rise of social networks and online communities, group activities become increasingly common, which promotes the development of group recommendations. As the first step of group recommendation, group discovery aims to identify potential groups from users. Current group discovery methods often fail to consider behavior preferences and social connections simultaneously and may not be trained in a group-discovery-oriented manner. To address the above problems, we propose a novel group discovery method called BSGD based on users' behaviors and socialization, which introduces three tasks and implements group-discovery-oriented end-to-end training through multi-task joint training. The experiment results show that the proposed method has an excellent performance in both group discovery and gains in group recommendation on two real-world datasets.