Parabolic permutation representations of the groups \(^2F_4(q)\) and \(^3D_4(q^3)\) (Q1581460)

An important class of permutation representations of groups of Lie type is formed by parabolic representations, i. e., representations on cosets of parabolic subgroups. For finite simple groups of twisted Lie type, the faithful parabolic representations of minimal degree were studied by \textit{A. V. Vasil'ev} [Algebra Logika 37, No. 1, 17-35 (1998; Zbl 0941.20007)]. In the present paper, the degrees, ranks, subdegrees, and double centralizers of the primitive parabolic representations of nonminimal degree of the twisted groups \(^2F_4(q)\) and \(^3D_4(q^3)\) are found.