ATLAS: Linear group L2(49)
Order = 58800 = 24.3.52.72.
Mult = 2.
Out = 22.
Standard generators of L2(49) are a
and b where
a has order 2, b has order 3,
ab has order 25 and ababb has order 24.
Standard generators of the double cover 2.L2(49) = SL2(49)
are preimages A and B where
A has order 3 and AB has order 25.
An outer automorphism of type 2a of order 2 may be obtained by mapping (a, b) to (a, bb).
Presentations for L2(49) ... in terms of their standard generators are given below.
< a, b | a2 = b3 = (ababab-1)4 = (ab)6(ab-1)2(ab)3(abab-1)2(ab)4(ab-1)2 = 1 >.
The representations of L2(49) available are:
- All primitive permutation representations.
-
Permutations on 50 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 175a points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 175b points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 175b points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 980b points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 1176 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 1225 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 3 over GF(49):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 3 over GF(49):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 4 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of 2.L2(49) = SL2(49) available are:
-
Dimension 2 over GF(49):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 2 over GF(49):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The maximal subgroups of L2(49) include the following:
- 72:24.
Order: 1176.
Index: 50.
- PGL2(7).
Order: 336.
Index: 175.
- PGL2(7).
Order: 336.
Index: 175.
- A5.
Order: 60.
Index: 980.
- A5.
Order: 60.
Index: 980.
- D50.
Order: 50.
Index: 1176.
- D48.
Order: 48.
Index: 1225.
Go to main ATLAS (version 2.0) page.
Go to linear groups page.
Go to old L2(49) page - ATLAS version 1.
Anonymous ftp access is also available.
See here for details.
Version 2.0 file created on 16th January 2002, from Version 1 file last modified on 08.10.98.
Last updated 16.01.02 by RAW.
Information checked to
Level 0 on 16.01.02 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.