Cross-domain recommendation (CDR) tasks aim to improve the recommendation performance in domains with limited data by leveraging information from other domains. The goal is to capture and then transfer the knowledge available in the information-rich domains to the sparse domain. However, traditional CDR techniques struggle when there is little overlap among users, making it hard to map preferences accurately. This paper introduces the Group-aided Cross-Domain Recommender System (gCDR), which integrates group information from overlapping users across domains. By identifying and utilizing shared preference patterns among user groups, gCDR enhances recommendation stability even with minimal user overlap across domains. To assess the efficacy of our gCDR framework, we have conducted experiments across two key settings, one with overlapping users and the other with overlapping items. For both scenarios, the gCDR model outperforms the best benchmark model over diverse evaluation metrics by a significant margin. The results highlight the importance of group dynamics in optimizing cross-domain recommendations and provide a robust solution to enhance recommender system performance in different data environments.