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The largest automorphism group of del Pezzo surface of degree $2$ without points
We construct an example of a field and a smooth del Pezzo surface of degree $2$ over this field without points such that its automorphism group is isomorphic to $\mathrm{PSL}_2(\mathbb{F}_7) \times \mathbb{Z}/2\mathbb{Z},$ which is the largest possible automorphism group of del Pezzo surfaces of deg
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