ATLAS: Linear group L_{2}(181)
Order = 2964780 = 2^{2}.3^{2}.5.7.13.181.
Mult = 2.
Out = 2.
The following information is available for L_{2}(181):
Standard generators of L_{2}(181) are a of
order 2, b of order 3 such that ab has order 181.
Standard generators of the double cover
2.L_{2}(181) = SL_{2}(181) are preimages
A and B such that B has order 3 and
AB has order 181.
Standard generators of L_{2}(181):2 = PGL_{2}(181) are not yet defined.
Standard generators of the double cover 2.L_{2}(181):2 = 2.PGL_{2}(181) are not yet defined.
Automorphisms
An outer automorphism of L_{2}(181) of
order 2 may be obtained by mapping (a, b) to
(a, b^{ababababab2ab2abab}).
The representations of L_{2}(181) available are:
 Some primitive permutation representations

Permutations on 182 points:
a and
b (GAP).
 Some matrix representations in characteristic 0:

Dimension 181 over Z:
a and b (GAP).

Dimension 182 over Z(z90) (monomial):
a and b (GAP).
The representations of 2.L_{2}(181) = SL_{2}(181) available are:
 Some matrix representations in characteristic 0:

Dimension 182 over Z(z180) (monomial):
A and B (GAP).
The representations of L_{2}(181):2 = PGL_{2}(181) available are:
The representations of 2.L_{2}(181):2 available are:
Maximal subgroups
The maximal subgroups of L_{2}(181) are as follows.

181:90, with generators
a, ab^{2}abababababab^{2}ab^{2}ab

D_{182}, with generators
a, a^{abab}

D_{180}, with generators
a, a^{abab2ababab}

A_{5}, with standard generators
a, b^{ababab}

A_{5}, with standard generators
a, b^{ababab2ababab}
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Version 2.0 created on 28th April 2004.
Last updated 30.04.04 by SN.