$G$-birational rigidity of the $G$-Fano variety ${\mathbb{P}}^1\times {\mathbb{P}}^1\times {\mathbb{P}}^1$

We determine the $G$-birational rigidity of the $G$-Fano variety ${\mathbb{P}}^1\times {\mathbb{P}}^1\times {\mathbb{P}}^1$ for all finite subgroups $G$ of $\mathrm{A}\mathrm{u}\mathrm{t}({\mathbb{P}}^1\times {\mathbb{P}}^1\times {\mathbb{P}}^1)$.