Groups are the primary entities that make up a crowd. Understanding group-level dynamics and properties is thus scientifically important and practically useful in a wide range of applications, especially for crowd understanding. In this study we show that fundamental group-level properties, such as intra-group stability and inter-group conflict, can be systematically quantified by visual descriptors. This is made possible through learning a novel Collective Transition prior, which leads to a robust approach for group segregation in public spaces. From the prior, we further devise a rich set of group property visual descriptors. These descriptors are scene-independent, and can be effectively applied to public-scene with variety of crowd densities and distributions. Extensive experiments on hundreds of public scene video clips demonstrate that such property descriptors are not only useful but also necessary for group state analysis and crowd scene understanding.