  In a sample of 58 million $J/\psi$ events collected with the BES II detector,
the process J/$\psi\to\gamma\eta_c$ is observed in five different decay
channels: $\gamma K^+K^-\pi^+\pi^-$, $\gamma\pi^+\pi^-\pi^+\pi^-$, $\gamma
K^\pm K^0_S \pi^\mp$ (with $K^0_S\to\pi^+\pi^-$), $\gamma \phi\phi$ (with
$\phi\to K^+K^-$) and $\gamma p\bar{p}$. From a combined fit of all five
channels, we determine the mass and full-width of $\eta_c$ to be
$m_{\eta_c}=2977.5\pm1.0 ({stat.})\pm1.2 ({syst.})$ MeV/$c^2$ and
$\Gamma_{\eta_c} = 17.0\pm3.7 ({stat.})\pm7.4 ({syst.})$ MeV/$c^2$.
