  We calculate the J/{\psi} mass, leptonic width and radiative decay rate to
\gamma \eta_c from lattice QCD including u, d and s quarks in the sea for the
first time. We use the Highly Improved Staggered Quark formalism and
nonperturbatively normalised vector currents for the leptonic and radiative
decay rates. Our results are: M_{J/\psi} -M_{\eta_c} = 116.5(3.2) MeV;
\Gamma(J/{\psi} to e^+e^-) = 5.48(16) keV; \Gamma(J/{\psi} to \gamma \eta_c) =
2.49(19) keV. The first two are in good agreement with experiment, with
\Gamma(J/{\psi} to e^+e^-) providing a test of a decay matrix element in QCD,
independent of CKM uncertainties, to 2%. At the same time results for the time
moments of the correlation function can be compared to values from the charm
contribution to \Gamma(e^+e^- to hadrons), giving a 1.5% test of QCD. Our
results show that an improved experimental error would enable a similarly
strong test from \Gamma(J/{\psi} to \gamma \eta_c).
