> < ^ Date: Tue, 19 Nov 2002 09:03:38 +0100
> < ^ From: Thomas Breuer <Thomas.Breuer@Math.RWTH-Aachen.DE >
< ^ Subject: Re: Maxes for Fi24

Dear GAP Forum,

Christopher Bates asked

Does anyone know if the latest version of GAP has the maximal subgroup
information, in the 'Maxes' format, for Fi24' and Fi24. Version 4.2 appears not

The latest released version of GAP does not contain the character tables
of all maximal subgroups of these groups,
and thus also the `Maxes' entries for these groups are missing.

In the development version of the `ctbllib' package,
the character tables of the maximal subgroups of Fi24' are available.
I am planning a new release of this package for Christmas 2002.
(If wanted so, I can put a preliminary archive with the missing tables of
maximal subgroups of Fi24' on a suitable webpage.)

The character tables of maximal subgroups of Fi24 are not (yet) available
in the development version of the `ctbllib' package,
but it will not be too difficult to compute them.
(However, I doubt that I will find time for adding them before Christmas.)

By the way,
if only the `Maxes' entry for Fi24 is of interest, without having access
to the tables, the list on p. 207 in the ATLAS of Finite group (plus the
confirmation of its completeness in the Appendix of the ATLAS of Brauer
Characters) describes the classes of maximal subgroups of Fi24.
They have the following structures.

Fi24', Fi23x2, (2x2.Fi22):2, S3xO8+(3):S3, O10-(2).2, 3^7.O7(3):2,
3_+^(1+10):(2xU5(2):2), 2^12.M24, (2x2^2.U6(2)):S3,
2_+^(1+12).3U4(3).(2^2)_{122}, 3^2.3^4.3^8.(S5x2S4), S4xO8+(2).S3,
7_+^(1+2):(6xS3).2, 2^(3+12).(L3(2)xS6), 2^(7+8).S3xA8, (S3xS3xG2(3)):2,
S5xS9, 7:6xS7, 29:28, 3^3.[3^10].(L3(3)x2^2), and S6xL2(8):3.

The list of maximal subgroups of Fi24' and Fi24 has been published in

Stephen A. Linton and Robert A. Wilson,
The maximal subgroups of the Fischer groups $Fi_{24}$ and $Fi'_{24}$,
Proc. London Math.  Soc. (3) 63 (1991), no. 1, 113--164.

All the best,

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