There is an explosion of community-generated multimedia content available online. In particular, Flickr constitutes a 200-million photo sharing system where users participate following a variety of social motivations and themes. Flickr groups are increasingly used to facilitate the explicit definition of communities sharing common interests, which translates into large amounts of content (e.g. pictures and associated tags) about specific subjects. However, to our knowledge, an in-depth analysis of user behavior in Flickr groups remains open, as does the existence of effective tools to find relevant groups. Using a sample of about 7 million user-photos and about 51000 Flickr groups, we present a novel statistical group analysis that highlights relevant patterns of photo-to-group sharing practices. Furthermore, we propose a novel topic-based representation model for groups, computed from aggregated group tags. Groups are represented as multinomial distributions over semantically meaningful latent topics learned via unsupervised probabilistic topic modeling. We show this representation to be useful for automatically discovering groups of groups and topic expert-groups, for designing new group-search strategies, and for obtaining new insights of the semantic structure of Flickr groups.