Using Quillen's description of cyclic cohomology in terms of traces on algebra extensions and Burghelea's computation of the cyclic homology of the group algebra of a group Π, we derive a description of the homology of Π with coefficients in a field of characteristic 0 as the inverse limit of a functor on the category of extensions of Π.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 1, pp.237-257.