The growing popularity of group activities increased the need to develop methods for providing recommendations to a group of users based on the collective preferences of the group members. Several group recommender systems have been proposed, but these methods often struggle due to sparsity and high-dimensionality of the available data, common in many real-world applications. In this paper, we propose a group recommender system called Group Soft-Impute SVD, which leverages soft-impute singular value decomposition to enhance group recommendations. This approach addresses the challenge of sparse high-dimensional data using low-rank matrix completion. We compared the performance of Group Soft-Impute SVD with Group MF based approaches and found that our method outperforms the baselines in recall for small user groups while achieving comparable results across all group sizes when tasked on Goodbooks, Movielens, and Synthetic datasets. Furthermore, our method recovers lower matrix ranks than the baselines, demonstrating its effectiveness in handling high-dimensional data.