K3 surfaces with an automorphism of order 66, the maximum possible

In each characteristic p≠2,3, it was shown in a previous work that the order of an automorphism of a K3 surface is bounded by 66, if finite. Here, it is shown that in each characteristic p≠2,3 a K3 surface with a cyclic action of order 66 is unique up to isomorphism. The equation of the unique surface is given explicitly in the tame case (p∤66) and in the wild case (p=11).