  We define an extended Bloch group and show it is naturally isomorphic to
H_3(PSL(2,C)^\delta ;Z). Using the Rogers dilogarithm function this leads to an
exact simplicial formula for the universal Cheeger-Chern-Simons class on this
homology group. It also leads to an independent proof of the analytic
relationship between volume and Chern-Simons invariant of hyperbolic
3-manifolds conjectured by Neumann and Zagier [Topology 1985] and proved by
Yoshida [Invent. Math. 1985] as well as effective formulae for the Chern-Simons
invariant of a hyperbolic 3-manifold.
