The Shintani descents of Suzuki groups and their consequences

The main aim of this paper is to associate to every cuspidal unipotent character of the Suzuki group its root of unity and to show that the Fourier matrix defined by Geck and Malle for the family of the cuspidal unipotent characters of this group satisfies a conjecture of Digne and Michel. To this end we determine the character table of the extension of Sp4 by the exceptional graph automorphism in characteristic 2 and compute the Shintani descents of Suzuki groups.