ATLAS: Linear group L_{2}(179)
Order = 2867580 = 2^{2}.3^{2}.5.89.179.
Mult = 2.
Out = 2.
The following information is available for L_{2}(179):
Standard generators of L_{2}(179) are a of
order 2, b of order 3 such that ab has order 179.
Standard generators of the double cover
2.L_{2}(179) = SL_{2}(179) are preimages
A and B such that B has order 3 and
AB has order 179.
Standard generators of L_{2}(179):2 = PGL_{2}(179) are not yet defined.
Standard generators of the double cover 2.L_{2}(179):2 = 2.PGL_{2}(179) are not yet defined.
Automorphisms
An outer automorphism of L_{2}(179) of
order 2 may be obtained by mapping (a, b) to
(a, b^{ab2ab2ab2abab2ababab2ab2abab}).
The representations of L_{2}(179) available are:
 Some primitive permutation representations

Permutations on 180 points:
a and
b (GAP).
 Some matrix representations in characteristic 0:

Dimension 179 over Z:
a and b (GAP).

Dimension 180 over Z(z89) (monomial):
a and b (GAP).
The representations of 2.L_{2}(179) = SL_{2}(179) available are:
 Some matrix representations in characteristic 0:

Dimension 180 over Z(z178) (monomial):
A and B (GAP).
The representations of L_{2}(179):2 = PGL_{2}(179) available are:
The representations of 2.L_{2}(179):2 available are:
Maximal subgroups
The maximal subgroups of L_{2}(179) are as follows.

179:89, with generators
ab^{2}, abab^{2}abab^{2}abab^{2}ab^{2}abab^{2}ababab

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

D_{178}, with generators
a, a^{ab}

A_{5}, with standard generators
a, b^{ab2abababab2ab}

A_{5}, with standard generators
a, b^{ab2ab2ab2ab2ab2ab}
Go to main ATLAS (version 2.0) page.
Go to linear groups page.
Anonymous ftp access is also available.
See here for details.
Version 2.0 created on 28th April 2004.
Last updated 30.04.04 by SN.