  We define an extended Bloch group and show it is 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-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 manifolds
conjectured in \cite{neumann-zagier} and proved in \cite{yoshida}, as well as
an effective formula for the Chern-Simons invariant of a hyperbolic manifold.
