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# Data for Finite Groups of Lie Type and Related Algebraic Groups

The following results are answers to questions I got from various people. Tell me if you have any comments, suggestions, further questions, ...

Possible topics for this section are all sorts of information on conjugacy classes, structures of certain subgroups and representations. The emphasis is on results of computations, in particular for the series of exceptional groups of Lie type.

To get started we have for now:

- Numbers of conjugacy classes, semisimple classes, semisimple elements, ... in some series of groups.
- All degrees of complex irreducible representations and their multiplicities for many series of groups of semisimple rank less than 9.
- Tables of weight multiplicities of small degree representations in defining characteristic.
- A description of the conjugacy classes of elements of orders 2 and 3 in exceptional groups of Lie type.
- Centralizers and numbers of semisimple classes in exceptional groups of Lie type
- Conjugacy class lengths and character degrees for
^{2}E_{6}(2). - Conjugacy class lengths and character degrees for
E
_{7}(2). - Conjugacy class lengths and character degrees for
E
_{8}(2). - extraGenTabGLGU.tar.gz is an archive
containing the generic character tables of GL
_{n}(q) and GU_{n}(q) for n = 4,5,6. These extra tables can be used with both versions of`cheviem`

(that is with`MapleV.3`

, or with`Maple 8`

and higher, see the CHEVIE page. Just unpack the archive in the`tables`

subdirectory of your`cheviem`

installation. - Permutation representations, each on 16575 points, of the groups O_8^+(4):3 (328 kB) and O_8^+(4):S_3 (436 kB) as GAP-readable files.
- Permutation representations of O_8^+(5) (0.7MB), O_8^+(5).3 (1.0MB) and O_8^+(5).S_3 (1.3MB) on 117000 points and permutation representations of 2^2.O_8^+(5) = Spin_8(5) (1.4MB), 2^2.O_8^+(5).3 = Spin_8(5).3 (2.1MB) and 2^2.O_8^+(5).S_3 = Spin_8(5).S_3 (2.8MB) on 234000 points. The files are gzip'ed and GAP-readable.
- Permutation representation of the simple group ^2E_6(2) (26.5MB) on 3968055 points, and permutation representation of its maximal subgroup N(3c) (30kB) on 2187 points and the corresponding permutation character of ^2E_6(2).

Last updated: Wed Dec 19 15:31:04 2018 (CET)