ATLAS: Lyons group Ly

Order = 51765179004000000 = 28.37.56.7.11.31.37.67.
Mult = 1.
Out = 1.

The following information is available for Ly:


Standard generators

Standard generators of the Lyons group Ly are a and b where a has order 2, b is in class 5A, ab has order 14 and abababb has order 67.

Black box algorithms

Finding generators

To find standard generators for Ly:

This algorithm is available in computer readable format: finder for Ly.

Checking generators

To check that elements x and y of Ly are standard generators:

This algorithm is available in computer readable format: checker for Ly.

Representations

The representations of Ly available are:

Maximal subgroups

The maximal subgroups of Ly are:

Conjugacy classes

A set of generators for the maximal cyclic subgroups can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements.
Problems of algebraic conjugacy are dealt with as follows: the choice of classes for elements of orders 21, 31, 37, 40, 42, and 67 is the one used by Mueller, Neunhoeffer, Roehr and Wilson when determining the irrationalities in the character tables mod 37 and 67. In some cases this means that we only know the traces on class representatives, and not the Brauer character values, since we are not able to calculate the canonical lifting of eigenvalues. The choice of classes for the elements of orders 11, 22 and 33 is made independently, using the representation of degree 2480 in characteristic 0 (or 2, or ...).
Main ATLAS page Go to main ATLAS (version 2.0) page.
Sporadic groups page Go to sporadic groups page.
Old Ly page Go to old Ly page - ATLAS version 1.
ftp access Anonymous ftp access is also available on for.mat.bham.ac.uk - username atlasftp, password atlasftp.

Version 2.0 created on 7th June 2000.
Last updated 7.1.05 by SJN.
Information checked to Level 0 on 07.06.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.