Using the inclusive photon spectrum based on a data sample collected at the $J/psi$ peak with the KEDR detector at the VEPP-4M $e^+e^-$ collider, we measured the rate of the radiative decay $J/psitogammaeta_{rm c}$ as well as $eta_{rm c}$ mass and width. Taking into account an asymmetric photon lineshape we obtained $Gamma^0_{gammaeta_{rm c}}=2.98pm0.18 phantom{|}^{+0.15}_{-0.33}$ keV, $M_{eta_{rm c}} = 2983.5 pm 1.4 phantom{|}^{+1.6}_{-3.6}$ MeV/$c^2$, $Gamma_{eta_{rm c}} = 27.2 pm 3.1 phantom{|}^{+5.4}_{-2.6}$ MeV.