ATLAS: Linear group L4(4)
Order = 987033600 = 212.34.52.7.17.
Mult = 1.
Out = 22.
The following information is available for L4(4):
Standard generators of L4(4) are a and b where
a is in class 2B, b is in class 4A and ab has order 30.
Standard generators of L4(4):21 are not defined.
Standard generators of L4(4):22 are not defined.
Standard generators of L4(4):23 are not defined.
Standard generators of L4(4):22 are not defined.
To find standard generators of L4(4):
- Find an element of order 2, 4, 6 or 10 and power it up to give an
involution x
- Look for a random element z such that [x, z] has
order greater than 5. If none can be found after two attempts, go
back to step 1. Otherwise, we know x is a 2B element.
- Find an element of order 12 and power it up to give an element
t in class 4A.
- Find a conjugate y of t such that xy has order 30.
- The elements x and y are standard generators.
The representations of L4(4) available are:
-
Permutations on 85a points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 85b 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.