  Based on a data sample of $(27.08 \pm 0.14 ) \times 10^8~\psi(3686)$ events
collected with the BESIII detector at the BEPCII collider, the M1 transition
$\psi(3686) \to \gamma \eta_{c}(2S)$ with $\eta_{c}(2S) \to K\bar{K}\pi$ is
studied, where $K\bar{K}\pi$ is $K^{+} K^{-} \pi^{0}$ or
$K_{S}^{0}K^{\pm}\pi^{\mp}$. The mass and width of the $\eta_{c}(2S)$ are
measured to be $(3637.8 \pm 0.8 (\rm {stat}) \pm 0.2 (\rm {syst}))$ MeV/$c^{2}$
and $(10.5 \pm 1.7 (\rm {stat}) \pm 3.5 (\rm {syst}))$ MeV, respectively. The
product branching fraction $\mathcal{B}\left(\psi(3686) \rightarrow \gamma
\eta_{c}(2 S)\right) \times \mathcal{B}(\eta_{c}(2 S) \rightarrow K \bar{K}
\pi)$ is determined to be $(0.97 \pm 0.06 (\rm {stat}) \pm 0.09 (\rm {syst}))
\times 10^{-5}$. Using $\mathcal{BR}(\eta_{c}(2S)\to
K\bar{K}\pi)=(1.86^{+0.68}_{-0.49})\%$, we obtain the branching fraction of the
radiative transition to be $\mathcal{BR}(\psi(3686) \to \gamma \eta_{c}(2S)) =
(5.2 \pm 0.3 (\rm {stat}) \pm 0.5 (\rm {syst}) ^{+1.9}_{-1.4} (extr)) \times
10^{-4}$, where the third uncertainty is due to the quoted
$\mathcal{BR}(\eta_{c}(2S) \to K\bar{K}\pi)$.
