Using a sample of 106 million psi(3686) events collected with the BESIII detector at the BEPCII storage ring, we have made the first measurement of the M1 transition between the radially excited charmonium S-wave spin-triplet and the radially excited S-wave spin-singlet states: psi(3686)togammaeta_c(2S). Analyses of the processes psi(2S)to gammaeta_c(2S) with eta_c(2S)to K_S^0 Kpi and K^+K^-pi^0 gave an eta_c(2S) signal with a statistical significance of greater than 10 standard deviations under a wide range of assumptions about the signal and background properties. The data are used to obtain measurements of the eta_c(2S) mass (M(eta_c(2S))=3637.6pm 2.9_mathrm{stat}pm 1.6_mathrm{sys} MeV/c^2), width (Gamma(eta_c(2S))=16.9pm 6.4_mathrm{stat}pm 4.8_mathrm{sys} MeV), and the product branching fraction (BR(psi(3686)to gammaeta_c(2S))times BR(eta_c(2S)to Kbar Kpi) = (1.30pm 0.20_mathrm{stat}pm 0.30_mathrm{sys})times 10^{-5}). Combining our result with a BaBar measurement of BR(eta_c(2S)to Kbar K pi), we find the branching fraction of the M1 transition to be BR(psi(3686)togammaeta_c(2S)) = (6.8pm 1.1_mathrm{stat}pm 4.5_mathrm{sys})times 10^{-4}.
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