Emerging event-based social networks (EBSNs), such as Meetup, have grown rapidly and become popular in recent years. EBSNs differ from conventional social networks such as Facebook in that they not only involve online social interactions but also include offline, in-person interactions. Thus, EBSNs are naturally heterogeneous and possess more valuable social information. Group recommendations in EBSNs are typically only based on the interest information filled in by users, or friends' group information. Both these methods may not well reflect users' real intentions. In this study, we propose a recommender system to predict groups that may interest EBSN users, based on a novel heterogeneous augmented graph method and a random walk with restart algorithm. In this approach, online and offline social interactions are combined into a single heterogeneous augmented graph capturing all useful relationships, including user-to-group relationships, user-to-event relationships, user-to-attribute relationships, and groupto-attribute relationships, and among others. To our knowledge, this work is the first attempt to apply a random walk algorithm into group recommendation in EBSNs. Extensive experiments on Meetup datasets demonstrate that our proposed recommender system achieves better results in terms of recall, precision, F-Measure and MRR metrics in comparison with the other four commonly used algorithms, including random recommendation, interest-based recommendation, interest-and neighborhood-based recommendation, and Katz Centrality. The significant recommendation performance of our approach may further enhance user satisfaction of EBSNs. Moreover, our approach to group recommendation may also be extended to other recommendation-related applications such as event or friend recommendation.