Condensed mathematics provides a convenient framework for studying algebraic objects that carry a topology, and in particular enables the construction of a derived fixed point functor on continuous GG-modules for a topological group GG. In this talk, I will compare condensed group cohomology of a topological group with its continuous group cohomology (defined via continuous cochains), as well as with the(condensed/singular/sheaf) cohomology of its classifying space. For locally profinite groups and solid (e.g., locally profinite) continuous GG-modules, continuous group cohomology is isomorphic to condensed group cohomology. The same holds for locally compact, paracompact topological groups with finite-dimensional vector spaces as coefficients. In general, however, condensed group cohomology is a more refined invariant. I will explain that nonetheless, continuous group cohomology with solid coefficients can be described as Ext groups in the condensed setup for a broad class of groups.