Using a sample of 106×10(6) ψ(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: ψ(3686)→γη(c)(2S). Analyses of the processes ψ(3686)→γη(c)(2S) with η(c)(2S)→K(S)(0)K(±)π(∓) and K(+)K(-)π(0) give an η(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 η(c)(2S) mass (M(η(c)(2S))=3637.6±2.9(stat)±1.6(syst) MeV/c(2)), width (Γ(η(c)(2S))=16.9±6.4(stat)±4.8(syst) MeV), and the product branching-fraction (B(ψ(3686)→γη(c)(2S))×B(η(c)(2S)→KKπ)=(1.30±0.20(stat)±0.30(syst))×10(-5)). Combining our result with a BABAR measurement of B(η(c)(2S)→KKπ), we find the branching fraction of the M1 transition to be B(ψ(3686)→γη(c)(2S))=(6.8±1.1(stat)±4.5(syst))×10(-4).