ATLAS: Linear group L_{3}(11)
Order = 212427600 = 2^{4}.3.5^{2}.7.11^{3}.19.
Mult = 1.
Out = 2.
See also ATLAS of Finite Groups, p91.
Standard generators of L_{3}(11) are a and b where
a has order 3, b is in class 11A, ab has order 120,
abb has order 10 and ababb has order 40. The last two
conditions can be replaced by ab^{5} has order 55.
Standard generators of L_{3}(11):2 are not defined.
NB: Class 11A is the class of transvections in the natural representation of
L_{3}(11).
Presentations for L_{3}(11) and L_{3}(11):2 on their standard generators are given below.
< a, b  a^{3} = b^{11} = aba^{1}bab^{2}a^{1}baba^{1}b^{2} = (abab^{1})^{3}a^{1}b^{2}a^{1}b^{1} = 1 >.
These presentations are available in Magma format as follows:
L3(11) on a and b and
L3(11):2 on c and d.
The representations of L_{3}(11) available are

Permutations on 133 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 132 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 132 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 132 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 131 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 3 over GF(11):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
 the natural representation.

Dimension 131 over GF(19):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
 Dimension 132 over Z:
a and b (GAP).
The representations of L_{3}(11):2 available are
Go to main ATLAS (version 2.0) page.
Go to linear groups page.
Go to old L3(11) page  ATLAS version 1.
Anonymous ftp access is also available on
sylow.mat.bham.ac.uk.9
Version 2.0 created on 30th July 1999.
Last updated 04.13.04 by SJN.
Information checked to
Level 0 on 30.07.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.