This paper proposes both theoretical and empirical approaches to differentiating the community of inquiry (CoI) in online classes at individual and group levels. Following the example of research on organizational climate, it assesses the strength of shared perceptions of teaching presence, social presence, and cognitive presence. The paper develops a theory of composition that relates isomorphic constructs of these presences at the individual and class levels. Hypotheses are made about the agreement among students on the survey that is used to measure individual perceptions of the three presences of the CoI. These are tested using a set of statistics designed to measure the extent to which shared perceptions of these presences exist within classes. Strong evidence of shared perceptions is found, and potential practical and theoretical applications are described.