[GAP Forum] Maximal Subgroups

[Leandro Vendramin]

Hi Serkan,

> I would like to know how we can compute the maximal subgroups of mathieu group of degree 23 in gap.

The maximal subgroups of M23 are stored in the AtlasRep package.
The group M23 has 7 maximal subgroups. For example, the following code
can be used to obtain the 4th maximal subgroup of M23 (which is
isomorphic to A8, see for example the ATLAS of finite groups:
http://brauer.maths.qmul.ac.uk/Atlas/v3/lookup?target=m23).

gap> LoadPackage("atlasrep");
gap> N := 4;
gap> gr := Group(AtlasGenerators("M23", 1, N).generators);
Group([ (1,4)(5,11)(6,18)(7,10)(13,22)(14,20)(15,21)(16,19),
(1,15,17,18)(2,9,22,3)(4,8,23,13)(5,7)(6,12)(11,19,14,16) ])
gap> Size(gr);
20160

See the documentation of the AtlasRep package for more information on
the function AtlasGenerators.

Best regards,
Leandro