With the proliferation of social media, a growing number of users search for and join group activities in their daily life. This develops a need for the study on the group identification (GI) task, i.e., recommending groups to users. The major challenge in this task is how to predict users' preferences for groups based on not only previous group participation of users but also users' interests in items. Although recent developments in Graph Neural Networks (GNNs) accomplish embedding multiple types of objects in graph-based recommender systems, they, however, fail to address this GI problem comprehensively. In this paper, we propose a novel framework named Group Identification via Transitional Hypergraph Convolution with Graph Self-supervised Learning (GTGS). We devise a novel transitional hypergraph convolution layer to leverage users' preferences for items as prior knowledge when seeking their group preferences. To construct comprehensive user/group representations for GI task, we design the cross-view self-supervised learning to encourage the intrinsic consistency between item and group preferences for each user, and the group-based regularization to enhance the distinction among group embeddings. Experimental results on three benchmark datasets verify the superiority of GTGS. Additional detailed investigations are conducted to demonstrate the effectiveness of the proposed framework.