We compute the conjugacy classes and character table of a Borel subgroup of the Ree groups 2 F 4 (2 2n+1 ) for all n 1 and prove that these Borel subgroups are M -groups. We determine the degrees of the irreducible characters of the Sylow-2-subgroups of 2 F 4 (2 2n+1 ) and show that the IsaacsMalle-Navarro version of the McKay conjecture holds for 2 F 4 (2 2n+1 ) in characteristic 2. For most of the calculations we use CHEVIE.
We compute the conjugacy classes of elements and the character tables of the maximal parabolic subgroups of the simple Ree groups 2 F 4(q 2 ). For one of the maximal parabolic subgroups, we find an irreducible character of the unipotent radical that does not extend to its inertia subgroup.
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