ATLAS: Linear group L_{4}(5)
Order = 7254000000 = 2^{7}.3^{2}.5^{6}.13.31.
Mult = 4.
Out = D_{8}.
The following information is available for L_{4}(5):
Standard generators of L_{4}(5) are a and b where
a has order 2, b is in class 3B, ab has order 39
and ababb has order 20.
To find standard generators of L_{4}(5):
 Find an element of even order and power it up to give an
involution x
 Look for an element of order 24 or 30 and power it up to give
an element t in class 3B.
 Find a conjugate y of t such that xy has order 39
and xyxyy has order 20.
 The elements x and y are standard generators.
The representations of L_{4}(5) available are:

Permutations on 156a points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 156b 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.