# ATLAS: Unitary group U6(3)

Order = 22837472432087040 = 213.315.5.72.13.61.
Mult = 2.
Out = 22.

The following information is available for U6(3):

### Standard generators

Standard generators of U6(3) are a and b where a is in class 2A, b has order 15, ab has order 91 and abb has order 14.

### Black box algorithms

To find standard generators of U6(3):
• Find an element x in class 2A, say by powering up an element of order 122.
• Find an element t of order 15, say by powering up an element of order 30, 60 or 120.
• Look for a conjugate y of t such that xy has order 91 and xyy has order 14.
• The elements x and y are standard generators.

### Representations

The representations of U6(3) available are:
• Some primitive permutation representations.
• Permutations on 22204 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 44226 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).

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

Version 2.0 file created on 4th August 2004.
Last updated 4.8.04 by SJN.