Frequent group activities of human beings have become an indispensable part in their daily life. Group recommendation can recommend satisfactory activities to group members in the recommender systems, and the key issue is how to aggregate preferences in different group members. Most existing group recommendation employed the predefined static aggregation strategies to aggregate the preferences of different group members, but these static strategies cannot simulate the dynamic group decision-making. Meanwhile, most of these methods depend on intuitions or assumptions to analyze the influence of group members and lack of convincing theoretical support. We argue that the influence of group members plays a particularly important role in group decision-making and it can better assist group profile modeling and perform more accurate group recommendation. To tackle the issue of preference aggregation for group recommendation, we propose a novel attentive aggregation representation learning method based on sociological theory for group recommendation, namely SIAGR (short for "Social Influence-based Attentive Group Recommendation"), which takes attention mechanisms and the popular method (BERT) as the aggregation representation for group profile modeling. Specifically, we analyze the influence of group members based on social identity theory and two-step flow theory and exploit an attentive mavens mining method. In addition, we develop a BERT-based representation method to learn the interaction of group members. Lastly, we complete the group recommendation under the neural collaborative filtering framework and verify the effectiveness of the proposed method by experimenting.