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 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.
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.
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.