Computing 2-cocycles for central extensions and relative difference sets

We present an algorithm to compute H² (G, U) for a finite group G and finite abelian group U (trivial G-module). The algorithm returns a generating set for the second cohomology group in terms of representative 2-cocycles, which are given explicitly. This information may be used to find presentations for corresponding central extensions of U by G. An application of the algorithm to the construction of relative (4t,2,4t,2t)-difference sets is given.