ATLAS: Unitary group U5(4)

Order = 53443952640000 = 220.32.54.13.17.41.
Mult = 5.
Out = 5:4.

The following information is available for U5(4):

Standard generators

Standard generators of U5(4) are a and b where a is in class 2A, b has order 12, ab has order 41 and abb has order 15.
Standard generators of 5.U5(4) are preimages A and B where A has order 2 and B has order 12.

Standard generators of U5(4):5 (and its covers) are not defined.
Standard generators of U5(4):5:2 (and its covers) are not defined.
Standard generators of U5(4):5:4 (and its covers) are not defined.

Black box algorithms

To find standard generators of U5(4):
• Find an element x in class 2A, say by powering up an element of order 8, 12, 20, 26 or 30.
• Find an element t of order 12.
• Look for a conjugate y of t such that xy has order 41 and xyy has order 15.
• The elements x and y are standard generators.

Representations

The representations of U5(4) available are:
• Some primitive permutation representations.
• Permutations on 17425 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 52480 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).

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