Using a low background data sample of \(9.7\times10^{5}\) \(J\psi\rightarrow\gamma\eta^\prime\), \(\eta^\prime\rightarrow\gamma\pi^+\pi^-\) events recorded with the BESIII detector at BEPCII, the decay dynamics of \(\eta^\prime\rightarrow\gamma\pi^+\pi^-\) are studied with both model-dependent and -independent approaches. The contributions of \(\omega\) and the \(\rho(770)-\omega\) interference are observed for the first time in both approaches. Additionally, a contribution from the box anomaly or the \(\rho(1450)\) resonance is required in the model-dependent approach, while the process specific part of the decay amplitude is determined in the model-independent approach.