ATLAS: Linear group L_{3}(13)
Order = 270178272 = 2^{5}.3^{2}.7.13^{3}.61.
Mult = 3.
Out = S_{3}.
The following information is available for L_{3}(13):
Standard generators of L_{3}(13) are a and b where
a has order 2, b has order 3, ab has order 61
and ababb has order 4. (Extra condition added 1/11/05.)
Standard generators of the triple cover
3.L_{3}(13) = SL_{3}(13) are not defined.
Standard generators of L_{3}(13):2 are not defined.
Standard generators of L_{3}(13):3 = PGL_{3}(13) are
not defined.
Standard generators of L_{3}(13):S_{3} are not defined.
To find standard generators of L_{3}(13):
 Find an element of even order. This powers up to a of order 2.
 Find an element of order divisible by 3. This powers up to t of
order 3.
 Find a conjugate b of t such that ab has order 61
and ababb has order 4.
 The elements a and b are standard generators.
The representations of L_{3}(13) available are:

Permutations on 183a points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP). (Corrected 1/11/05)

Permutations on 183b points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP). (Corrected 1/11/05)

Dimension 182 over Z:
a and b (GAP).

Dimension 183 over Z:
a and b (GAP).

Dimension 183b over Z[i]:
a and b (GAP).

Dimension 183c over Z[i]:
a and b (GAP).

Dimension 366 over Z:
a and b (GAP).
— reducible over Q(i).
The representations of 3.L_{3}(13) = SL_{3}(13) available are:
Go to main ATLAS (version 2.0) page.
Go to linear groups page.
Anonymous ftp access is also available.
See here for details.
Version 2.0 file created on 3rd August 2004.
Last updated 13.12.05 by JNB.