On the group of extensions for the bicrossed product construction for a locally compact group - Chapovsky, Yu.A.; Kalyuzhnyi, A.A.; Podkolzin, G.B. (Algebra and Discrete Mathematics, 2004)
For the cocycle bicrossed product construction
applied to a locally compact group and its two subgroups, we give
a simple description of the group of the corresponding extensions
in terms of the second cohomology group of a certain complex of
continuous functions on the group. Using this description, we find
pairs of continuous cocycles for two subgroups of the Heisenberg
group.