ATLAS: Linear group L_{2}(23)
Order = 6072.
Mult = 2.
Out = 2.
The following information is available for L_{2}(23):
Standard generators of L2(23) are a
and b where
a has order 2, b has order 3
and ab has order 23.
Standard generators of the double cover 2.L2(23) = SL2(23) are preimages
A
and B where
B has order 3
and AB has order 23.
Standard generators of L2(23).2 are c
and d where
c has order 2, d has order 3,
cd has order 22, and cdcdd has order 4.
Standard generators of either double cover 2.L2(23).2 are preimages
C
and D where
D has order 3.
An outer automorphism of L_{2}(23) may be obtained by
running
this program on the standard generators.
The representations of L_{2}(23) available are:

Permutations on 24 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
 All irreducibles in characteristic 2:

Dimension 11 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 11 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 22 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 24 over GF(32):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 24 over GF(32):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 24 over GF(32):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 24 over GF(32):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 24 over GF(32):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 22 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 23 over GF(11):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
 All irreducibles in characteristic 23:

Dimension 3 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 5 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 7 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 9 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 11 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 13 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 15 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 17 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 19 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 21 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 23 over GF(23):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of 2.L2(23) available are

Dimension 2 over GF(23):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
The representations of L2(23).2 available are

Dimension 22 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 3 over GF(23):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
The representations of 2.L2(23):2 (Not the Atlas group) available are

Dimension 2 over GF(23):
C and
D (Meataxe),
C and
D (Meataxe binary),
C and
D (GAP).
The maximal subgroups of L2(23) are as follows.
 23:11, with generators
???.
 S_{4}
 S_{4}
 D_{24}
 D_{22}
The maximal subgroups of L2(23):2 are as follows.
 L_{2}(23)
 23:22
 D_{48}
 D_{44}
A set of generators for the maximal cyclic subgroups of L2(23) can be obtained
by running this program on the standard
generators. All conjugacy classes can therefore be obtained as suitable
powers of these elements.
A set of generators for the maximal cyclic subgroups of L2(23):2 can be obtained
by running this program on the standard
generators. All conjugacy classes can therefore be obtained as suitable
powers of these elements.
Go to main ATLAS (version 2.0) page.
Go to linear groups page.
Go to old L2(23) page  ATLAS version 1.
Anonymous ftp access is also available.
See here for details.
Version 2.0 file created on 18th January 2002,
from Version 1 file last modified on 13.03.96.
Last updated 30.01.02 by RAW.
Information checked to
Level 0 on 18.01.02 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.