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Due to 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 ranking-based group identification (RGI) task, i.e., recommending groups to users. The major challenge in this task is how to effectively and efficiently leverage both the item interaction and group participation of users' online behaviors. Though recent developments of Graph Neural Networks (GNNs) succeed in simultaneously aggregating both social and user-item interaction, they however fail to comprehensively resolve this RGI task. In this paper, we propose a novel GNN-based framework named Contextualized Factorized Attention for Group identification (CFAG). We devise tripartite graph convolution layers to aggregate information from different types of neighborhoods among users, groups, and items. To cope with the data sparsity issue, we devise a novel propagation augmentation (PA) layer, which is based on our proposed factorized attention mechanism. PA layers efficiently learn the relatedness of non-neighbor nodes to improve the information propagation to users. Experimental results on three benchmark datasets verify the superiority of CFAG. Additional detailed investigations are conducted to demonstrate the effectiveness of the proposed framework.