Despite the recent interest in fairness-aware graph clustering, most existing community detection approaches have not yet been extended to include measures of fairness in the community detection process. In this paper, we introduce Fair-mod, a group fairness-aware method for community detection optimizing for both modularity and fairness. We evaluate our method on real-world social network datasets, highlighting the trade-offs between modularity and fairness. We also compare our approach with state-of-the-art fair graph clustering based on spectral methods.