Amplitude analysis of

Using (2712 ± 14) × 10 $\textit{ψ}$(3686) events collected with the BESIII detector, we perform the first amplitude analysis of the radiative decay within the mass region GeV/$\textit{c}$ . Employing a one-channel K-matrix approach for the description of the dynamics of the system, the data sample is well described with four poles for the $\textit{f}$ -wave and three poles for the $\textit{f}$ -wave. The determined pole positions are consistent with those of well-established resonance states. The observed $\textit{f}$ and $\textit{f}$ states are found to be in agreement with those produced in radiative $\textit{J/ψ}$ decays. The production behaviors of $\textit{f}$ and $\textit{f}$ poles in are qualified with their residues and the converted branching fractions. By comparing with decay, the ratios are determined, which provides crucial experimental inputs on the internal structure of the $\textit{f}$ states, especially their potential mixing with glueball components.