ATLAS: Linear group L_{2}(49)
Order = 58800 = 2^{4}.3.5^{2}.7^{2}.
Mult = 2.
Out = 2^{2}.
Standard generators of L_{2}(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.L_{2}(49) = SL_{2}(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 L_{2}(49) ... in terms of their standard generators are given below.
< a, b  a^{2} = b^{3} = (ababab^{1})^{4} = (ab)^{6}(ab^{1})^{2}(ab)^{3}(abab^{1})^{2}(ab)^{4}(ab^{1})^{2} = 1 >.
The representations of L_{2}(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.L_{2}(49) = SL_{2}(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 L_{2}(49) include the following:
 7^{2}:24.
Order: 1176.
Index: 50.
 PGL_{2}(7).
Order: 336.
Index: 175.
 PGL_{2}(7).
Order: 336.
Index: 175.
 A_{5}.
Order: 60.
Index: 980.
 A_{5}.
Order: 60.
Index: 980.
 D_{50}.
Order: 50.
Index: 1176.
 D_{48}.
Order: 48.
Index: 1225.
Go to main ATLAS (version 2.0) page.
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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.