ATLAS: Linear group L_{2}(157)
Order = 1934868 = 2^{2}.3.13.79.157.
Mult = 2.
Out = 2.
The following information is available for L_{2}(157):
Standard generators of L_{2}(157) are a of
order 2, b of order 3 such that ab has order 157.
Standard generators of the double cover
2.L_{2}(157) = SL_{2}(157) are preimages
A and B such that B has order 3 and
AB has order 157.
Standard generators of L_{2}(157):2 = PGL_{2}(157) are not yet defined.
Standard generators of the double cover 2.L_{2}(157):2 = 2.PGL_{2}(157) are not yet defined.
Automorphisms
An outer automorphism of L_{2}(157) of
order 2 may be obtained by mapping (a, b) to
(a, b^{ababababababab2ab2ab}).
The representations of L_{2}(157) available are:
 Some primitive permutation representations

Permutations on 158 points:
a and
b (GAP).
 Some matrix representations in characteristic 0:

Dimension 157 over Z:
a and b (GAP).

Dimension 158 over Z(z78) (monomial):
a and b (GAP).
The representations of 2.L_{2}(157) = SL_{2}(157) available are:
 Some matrix representations in characteristic 0:

Dimension 158 over Z(z156) (monomial):
A and B (GAP).
The representations of L_{2}(157):2 = PGL_{2}(157) available are:
The representations of 2.L_{2}(157):2 available are:
Maximal subgroups
The maximal subgroups of L_{2}(157) are as follows.
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Version 2.0 created on 28th April 2004.
Last updated 30.04.04 by SN.