ATLAS: Linear group L3(4), Mathieu group M21, L3(4) subpage

Order = 20160 = 26.32.5.7.
Mult = 3 × 4 × 4.
Out = 2 × S3 = D12.

The following information is available for covers of L3(4) = M21:


Standard generators


Presentations

A presentation of L3(4) on its standard generators is given below. (This one has as its relations powers of short words; it is not so good from a coset enumeration point of view.)

< a, b | a2 = b4 = (ab)7 = (ab2)5 = (abab2)7 = (ababab2ab-1)5 = 1 >.

L3(4) on a and b.

Representations

NB: Irreducible, but not absolutely irreducible representations that contain absolutely irreducible constituents in 2 cohorts are ordered by their constituents in the `principal' cohort. The representations of L3(4) available are: The representations of 2.L3(4) available are: The representations of 3.L3(4) available are: The representations of 41.L3(4) available are: The representations of 42.L3(4) available are: The representations of 6.L3(4) available are: The representations of 121.L3(4) available are: The representations of 122.L3(4) available are:

Maximal subgroups

The 9 classes of maximal subgroups of L3(4) = M21 are as follows: By coincidence, the W1-generators for each of the maximal L3(2)s produce them on their (2, 7, 4)-generators (which are unique up to automorphisms for L3(2)) and standard generators for L3(2) may be obtained as (x, xyy) where (x, y) are the (2, 7, 4)-generators. The conversions from W1 to standard generators have been made available here, here and here.

Conjugacy classes

Representatives of the 10 conjugacy classes of L3(4) = M21 are as follows: The following information is required and/or useful for the covering groups.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Linear groups page Go to linear groups page.
L3(4) - main page Go to main L3(4) page.
Old L3(4) page Go to old L3(4) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created (for main L3(4) page) on 19th September 2001.
Subpage last updated 22.02.02 by JNB.
Information checked to Level 0 on 19.09.01 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.