ATLAS: Linear group L2(23)
Order = 6072.
Mult = 2.
Out = 2.
The following information is available for L2(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 pre-images
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 pre-images
C
and D where
D has order 3.
An outer automorphism of L2(23) may be obtained by
running
this program on the standard generators.
The representations of L2(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
???.
- S4
- S4
- D24
- D22
The maximal subgroups of L2(23):2 are as follows.
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.