K3 surfaces with an order 50 automorphism

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In any characteristic different from 2 and 5, Kondō gave an example of a K3 surface with a purely non-symplectic automorphism of order 50. The surface was explicitly given as a double plane branched along a smooth sextic curve. In this note we show that, in any characteristic p≠ 2, 5, a K3 surface with a cyclic action of order 50 is isomorphic to the example of Kondō.