Character tables of parabolic subgroups of Steinbergʹs triality groups

We compute the conjugacy classes of elements and the character tables of the parabolic subgroups of Steinbergʹs triality groups , where q is a power of an odd prime. Our main tools are Clifford theory applied to the Levi decomposition of the parabolic subgroups and the decomposition of restrictions of the unipotent characters of . For many of the calculations we use the CHEVIE package.