ATLAS: Unitary group U4(4)

Order = 1018368000 = 212.32.53.13.17.
Mult = 1.
Out = 4.

The following information is available for U4(4):

Standard generators

Standard generators of U4(4) are a and b where a is in class 2A, b is in class 4B and ab has order 20.
Standard generators of U4(4):2 are not defined.
Standard generators of U4(4):4 are not defined.

Black box algorithms

Finding generators

To find standard generators of U4(4):

• Find an element of order 20 or 30 and power it up to give an element x in class 2A.
• Find an element t of order 4 (not by powering up). Hopefully t is in class 4B.
• Look for a conjugate y of t such that xy has order 20. If all the orders of xy seem to be 15 or less, t is probably in the wrong class, so go back to step 2.
• The elements x and y are standard generators.
This algorithm is available in computer readable format: finder for U4(4).

Checking generators

To check that elements x and y of U4(4) are standard generators:

• Check o(x) = 2
• Check o(y) = 4
• Check o(xy) = 20
• Check o(x(xy)10) = 3
This algorithm is available in computer readable format: checker for U4(4).

Representations

The representations of U4(4) available are:
• Some primitive permutation representations.

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Version 2.0 file created on 3rd August 2004.
Last updated 13.1.05 by SJN.