ATLAS: Linear group L_{2}(59)
Order = 102660 = 2^{2}.3.5.29.59.
Mult = 2.
Out = 2.
The following information is available for L_{2}(59):
Standard generators of L_{2}(59) are a of
order 2, b of order 3 such that ab has order 59.
Standard generators of the double cover
2.L_{2}(59) = SL_{2}(59) are preimages
A and B such that B has order 3 and
AB has order 59.
Standard generators of L_{2}(59):2 = PGL_{2}(59) are not yet defined.
Standard generators of the double cover 2.L_{2}(59):2 = 2.PGL_{2}(59) are not yet defined.
Automorphisms
An outer automorphism of L_{2}(59) of
order 2 may be obtained by mapping (a, b) to
(a, b^{ab2ab2ab2ab2abababab2ab}).
The representations of L_{2}(59) available are:
 Some primitive permutation representations

Permutations on 60 points:
a and
b (GAP).
 Some matrix representations in characteristic 0:

Dimension 59 over Z:
a and b (GAP).

Dimension 60 over Z(z29) (monomial):
a and b (GAP).
The representations of 2.L_{2}(59) = SL_{2}(59) available are:
 Some matrix representations in characteristic 0:

Dimension 60 over Z(z58) (monomial):
A and B (GAP).
The representations of L_{2}(59):2 = PGL_{2}(59) available are:
The representations of 2.L_{2}(59):2 available are:
Maximal subgroups
The maximal subgroups of L_{2}(59) are as follows.

59:29, with generators
ab^{2}, ababab^{2}abab^{2}ab^{2}ab^{2}ababab

D_{60}, with generators
a, a^{abab2ab2abab}

A_{5}, with standard generators
a, b^{abab2ab}

A_{5}, with standard generators
a, b^{ab2abab2}

D_{58}, with generators
a, a^{ab}
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Version 2.0 created on 28th April 2004.
Last updated 30.04.04 by SN.