Physiological synchrony is a particular phenomenon of physiological responses during a face-face conversation. However, while many previous studies proposed various physiological synchrony measures between interlocutors in dyadic conversations, very few works on computing physiological synchrony in small groups (three or more people). Besides, belongingness and satisfaction are two critical factors for humans to decide where group they want to stay. Therefore, we want to investigate and reveal the relationship between physiological synchrony and belongingness/satisfaction under group conversation in this preliminary work. We feed the physiology ofgroup members into a designed learnable graph structure with the group-level physiological synchrony and heart-related features computed from Photoplethysmography (PPG) signals. We then devise a Group-modulated Attentive Bi-directional Long ShortTerm Memory (GGA-BLSTM) model to recognize groups' three levels ofbelongingness and satisfaction (low, middle, and high). Finally, we evaluate the proposed method on our recently collected multimodal group interaction corpus (never published before), NTUBA. The results show that (1) the models trained jointly with the grouplevel physiological synchrony and the conventional heart-related features consistently outperforms the model only trained with the conventional features, and (2) the proposed model with a Graphstructure Group-modulated Attention mechanism (GGA), GGABLSTM, performs better than the robust baseline model, the attentive BLSTM. Finally, the GGA-BLSTM achieves a good unweighted average recall (UAR) of 73.3% and 82.1% on group satisfaction and belongingness classification tasks, respectively. In further analyses, we reveal the relationships between physiological synchrony and group satisfaction/belongingness.