ATLAS: Linear group L_{2}(83)
Order = 285852 = 2^{2}.3.7.41.83.
Mult = 2.
Out = 2.
The following information is available for L_{2}(83):
Standard generators of L_{2}(83) are a of
order 2, b of order 3 such that ab has order 83.
Standard generators of the double cover
2.L_{2}(83) = SL_{2}(83) are preimages
A and B such that B has order 3 and
AB has order 83.
Standard generators of L_{2}(83):2 = PGL_{2}(83) are not yet defined.
Standard generators of the double cover 2.L_{2}(83):2 = 2.PGL_{2}(83) are not yet defined.
Automorphisms
An outer automorphism of L_{2}(83) of
order 2 may be obtained by mapping (a, b) to
(a, b^{ababab2ab2ababab}).
The representations of L_{2}(83) available are:
 Some primitive permutation representations

Permutations on 84 points:
a and
b (GAP).
 Some matrix representations in characteristic 0:

Dimension 83 over Z:
a and b (GAP).

Dimension 84 over Z(z41) (monomial):
a and b (GAP).
The representations of 2.L_{2}(83) = SL_{2}(83) available are:
 Some matrix representations in characteristic 0:

Dimension 84 over Z(z82) (monomial):
A and B (GAP).
The representations of L_{2}(83):2 = PGL_{2}(83) available are:
The representations of 2.L_{2}(83):2 available are:
Maximal subgroups
The maximal subgroups of L_{2}(83) are as follows.
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Version 2.0 created on 28th April 2004.
Last updated 30.04.04 by SN.