> < ^ Date: Wed, 14 May 2003 09:17:19 +0200
> < ^ From: Thomas Breuer <Thomas.Breuer@Math.RWTH-Aachen.DE >
> < ^ Subject: Re: maximal subgroups

Dear GAP Forum,

Ahmad Erfanian wrote

I would like to use the function " ConjugacyClassesMaximalSubgroups " in
Gap, for groups PSL(5,2), PSL(6,2), PSL(7,2). But it seems that there is a
problem for running time or something else. I will be more grateful for any
help or comments.

As has been pointed out already, these groups are quite large.
For PSL(5,2), the maximal subgroups can be accessed quickly using the
table of marks which is contained in the GAP Library of Tables of Marks.

Load the data library if necessary (and possible)

gap> RequirePackage( "tomlib" );
true

Load the table of marks of PSL(5,2).

gap> tom:= TableOfMarks( "L5(2)" );
TableOfMarks( "L5(2)" )

It stores the group PSL(5,2), represented as a permutation group.

gap> g:= UnderlyingGroup( tom );
Group([ (4,5)(6,8)(7,9)(16,19)(18,21)(23,25)(26,27)(30,31),
(1,2,3,4,6)(5,7,10,13,16)(8,11,14,17,20)(9,12,15,18,22)(19,23,26,28,
30)(21,24,27,29,25) ])

Fetch the information about the positions of the classes of maximal subgroups
in a list of all classes of subgroups (and about the indices of normalizers.)

gap> maxesinfo:= MaximalSubgroupsTom( tom );
[ [ 1410, 1409, 1408, 1407, 1010 ], [ 31, 31, 155, 155, 64512 ] ]

Fetch one representative of each class of maximal subgroups,
as a subgroup of the stored group `g'.

gap> List( maxesinfo[1], i -> RepresentativeTom( tom, i ) );
[ Group([ (3,29)(6,8)(7,9)(13,28)(15,24)(18,21)(20,22)(26,27),
(1,8,5,3,2)(4,19,13,10,9)(6,20,17,14,11)(7,22,21,15,12)(16,31,28,27,
25)(18,23,29,26,24) ]),
Group([ (3,19)(4,22)(5,20)(13,31)(15,23)(16,29)(24,25)(28,30),
(1,2,3,4,6)(5,7,10,13,16)(8,11,14,17,20)(9,12,15,18,22)(19,23,26,28,
30)(21,24,27,29,25) ]),
Group([ (1,24)(4,9)(5,23)(6,7)(8,25)(10,28)(11,22)(12,29)(16,27)(18,
30)(19,31)(21,26),
(1,10,25,31)(2,23,30,14)(3,18,29,21)(4,5)(7,26,
15,28)(9,27,24,13)(12,16,17,19)(20,22) ]),
Group([ (1,24)(2,27)(3,16)(5,6)(7,23)(10,31)(11,22)(12,19)(13,30)(17,
18)(21,29)(26,28), (1,11,10,12)(2,14)(3,24,13,29)(4,5,30,23)(7,
26)(8,27,18,9)(15,22,20,28)(16,19,25,31) ]),
Group([
(1,30,21,3,17)(2,26,4,14,18)(5,20,10,19,24)(6,28,25,27,9)(7,23,
16,11,15)(8,12,22,29,13),
(1,8,23,10,27,30,9,4,26,29,5,17,2,12,21,
13,22,31,11,7,24,16,6,20,3,15,28,25,18,19,14) ]) ]

For the groups L6(2) and L7(2), precomputed tables of marks are not available
in GAP.
The structure of their maximal subgroups is listed explicitly for example at

http://www.mat.bham.ac.uk/atlas/v2.0/lin/L62/

and

http://www.mat.bham.ac.uk/atlas/v2.0/lin/L72/

Kind regards,
Thomas

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