1.6.42 Fields, Groups, Rings

condition: Let \( f\left(x_{1}, x_{2}, x_{3}, x_{4}\right)=x_{1} x_{2} x_{3} \). Prove that the set \[ G_{f}=\left\{\sigma \in S_{4} \mid f\left(x_{\sigma(1)}, x_{\sigma(2)}, x_{\sigma(3)}, x_{\sigma(4)}\right)=\right. \] \( \left.f\left(x_{1}, x_{2}, x_{3}, x_{4}\right)\right\} \) is a group.