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Group work is a prevalent activity in educational settings, where students are often divided into topic-specific groups based on their preferences. The grouping should reflect the students' aspirations as much as possible. Usually, the resulting groups should also be balanced in terms of protected attributes like gender or race since studies indicate that students might learn better in a diverse group. Moreover, balancing the group cardinalities is also an essential requirement for fair workload distribution across the groups. In this paper, we introduce the multi-fair capacitated (MFC) grouping problem that fairly partitions students into non-overlapping groups while ensuring balanced group cardinalities (with a lower bound and an upper bound), and maximizing the diversity of members in terms of protected attributes. We propose two approaches: a heuristic method and a knapsack-based method to obtain the MFC grouping. The experiments on a real dataset and a semi-synthetic dataset show that our proposed methods can satisfy students' preferences well and deliver balanced and diverse groups regarding cardinality and the protected attribute, respectively.