# ATLAS: Linear group L4(4)

Order = 987033600 = 212.34.52.7.17.
Mult = 1.
Out = 22.

The following information is available for L4(4):

### Standard generators

Standard generators of L4(4) are a and b where a is in class 2B, b is in class 4A and ab has order 30.

Standard generators of L4(4):21 are not defined.
Standard generators of L4(4):22 are not defined.
Standard generators of L4(4):23 are not defined.
Standard generators of L4(4):22 are not defined.

### Black box algorithms

To find standard generators of L4(4):
• Find an element of order 2, 4, 6 or 10 and power it up to give an involution x
• Look for a random element z such that [x, z] has order greater than 5. If none can be found after two attempts, go back to step 1. Otherwise, we know x is a 2B element.
• Find an element of order 12 and power it up to give an element t in class 4A.
• Find a conjugate y of t such that xy has order 30.
• The elements x and y are standard generators.

### Representations

The representations of L4(4) available are:

Go to main ATLAS (version 2.0) page.
Go to linear groups page.
Anonymous ftp access is also available. See here for details.

Version 2.0 file created on 3rd August 2004.
Last updated 3.8.04 by SJN.