An important task in exploring and analyzing real-world data sets is to detect unusual and interesting phenomena. In this paper, we study the group anomaly detection problem. Unlike traditional anomaly detection research that focuses on data points, our goal is to discover anomalous aggregated behaviors of groups of points. For this purpose, we propose the Flexible Genre Model (FGM). FGM is designed to characterize data groups at both the point level and the group level so as to detect various types of group anomalies. We evaluate the effectiveness of FGM on both synthetic and real data sets including images and turbulence data, and show that it is superior to existing approaches in detecting group anomalies.