ATLAS: Unitary group U4(5)
Order = 14742000000 = 27.34.56.7.13.
Mult = 2.
Out = 22.
The following information is available for U4(5):
Standard generators of U4(5) are a and b where
a is in class 2A, b is in class 4B and ab has order 9.
Standard generators of 2.U4(5) = SU4(5) are
preimages A and B where AB has order 9.
To find standard generators of U4(5):
- Find an element of order 8, 24 or 60 and power it up to give
an element x in class 2A and an element t in class 4B.
- Look for a conjugate y of t such that xy has order 9.
- The elements x and y are standard generators.
The representations of U4(5) available are:
-
Some primitive permutation representations.
-
Permutations on 756 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 1575 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
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Version 2.0 file created on 3rd August 2004.
Last updated 3.8.04 by SJN.