Social memory consists of two processes: the detection of familiar compared with novel conspecifics and the detailed recollection of past social episodes. We investigated the neural bases for these processes using calcium imaging of dorsal CA2 hippocampal pyramidal neurons, known to be important for social memory, during social/spatial encounters with novel conspecifics and familiar littermates. Whereas novel individuals were represented in a low-dimensional geometry that allows for generalization of social identity across different spatial locations and of location across different identities, littermates were represented in a higher-dimensional geometry that supports high-capacity memory storage. Moreover, familiarity was represented in an abstract format, independent of individual identity. The degree to which familiarity increased the dimensionality of CA2 representations for individual mice predicted their performance in a social novelty recognition memory test. Thus, by tuning the geometry of structured neural activity, CA2 is able to meet the demands of distinct social memory processes.