ATLAS: Unitary group U_{4}(4)
Order = 1018368000 = 2^{12}.3^{2}.5^{3}.13.17.
Mult = 1.
Out = 4.
The following information is available for U_{4}(4):
Standard generators of U_{4}(4) are a and b where
a is in class 2A, b is in class 4B and ab has order 20.
Standard generators of U_{4}(4):2 are not defined.
Standard generators of U_{4}(4):4 are not defined.
Finding generators
To find standard generators of U_{4}(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 U_{4}(4).
Checking generators
To check that elements x and y of U_{4}(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 U_{4}(4).
The representations of U_{4}(4) available are:

Some primitive permutation representations.

Permutations on 325 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 1040 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 1105 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 3264 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
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See here for details.
Version 2.0 file created on 3rd August 2004.
Last updated 13.1.05 by SJN.