Character tables of parabolic subgroups of Steinberg's triality groups

AbstractWe compute the conjugacy classes of elements and the character tables of the parabolic subgroups of Steinberg's triality groups D43(q), 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 D43(q). For many of the calculations we use the CHEVIE package