0 0 2 1 − 2 − 1 1 0 1 1 − 1 − 1 0 0 0 1 − 1

This article is to contribute to the classification of finite-dimensional complex pointed Hopf algebras with Weyl groups of E6, E7, F4, G2. Many papers are about the classification of finite dimensional pointed Hopf algebras, for example, [AS98, AS02, AS00, AS05, He06, AHS08, AG03, AFZ, AZ07, Gr00, Fa07, AF06, AF07, ZZC, ZC]. In these research ones need the centralizers and character tables of groups. In this paper we obtain the representatives of conjugacy classes of Weyl groups of E6, E7, F4, G2 and all character tables of centralizers of these representatives by means of software GAP. By the Cartan-Killing classification of simple Lie algebras over complex field the Weyl groups to be considered are W (Al), (l ≥ 1); W (Bl), (l ≥ 2); W (Cl), (l ≥ 2); W (Dl), (l ≥ 4); W (El), (8 ≥ l ≥ 6); W (Fl), (l = 4); W (Gl), (l = 2). It is otherwise desirable to do this in view of the importance of Weyl groups in the theories of Lie groups, Lie algebras and algebraic groups. For example, the irreducible representations of Weyl groups were obtained by Frobenius, Schur and Young. The conjugace classes of W (F4) were obtained by Wall [Wa63] and its character tables were obtained by Kondo [Ko65]. The conjugace classes and character tables of W (E6), W (E7) and W (E8) were obtained by Frame [Fr51]. Carter gave a unified description of the conjugace classes of Weyl groups of simple Lie algebras [Ca72].