In this paper, a system to determine the emotion of a group of people via facial expression analysis is proposed for the Waseda Entertainment Robots. General models and standard methods for emotion definition and recognition are briefly described, as well as strategies for computing the group global emotion, knowing the individual emotions of group members. This work is based on Ekman's extended 'Big Six' emotional model, popular in Computer Science and Affective Computing. Emotion recognition via facial expression analysis is performed with a cloud-computing based solution, using Microsoft Azure Cognitive services. First, the performances of both the Face API to detect faces, and Emotion API, to compute emotion via face expression analysis, are tested. After that, a solution to compute the emotion of a group of people has been implemented and its performances compared to human perceptions. This work presents concepts and strategies which can be generalized for applications within the scope of assistive robotics and, more broadly, affective computing, wherever it will be necessary to determine the emotion of a group of people.