The codegree of an irreducible character $\chi $ of a finite group G is $|G : \ker \chi |/\chi (1)$ . We show that the Ree group ${}^2G_2(q)$ , where $q = 3^{2f+1}$ , is determined up to isomorphism by its set of codegrees.

Given a generalized octagon which satisfies certain geometric conditions, we show that it must be isomorphic to the Ree--Tits octagon arisingnaturally from a Ree group of type $^2F_4$ over a perfect field of characteristic 2, in which the Frobenius automorphism has a square root.

1991 Mathematics Subject Classification: 51E12.