ATLAS: Linear group L_{2}(71)
Order = 178920 = 2^{3}.3^{2}.5.7.71.
Mult = 2.
Out = 2.
The following information is available for L_{2}(71):
Standard generators of L_{2}(71) are a of
order 2, b of order 3 such that ab has order 71.
Standard generators of the double cover
2.L_{2}(71) = SL_{2}(71) are preimages
A and B such that B has order 3 and
AB has order 71.
Standard generators of L_{2}(71):2 = PGL_{2}(71) are not yet defined.
Standard generators of the double cover 2.L_{2}(71):2 = 2.PGL_{2}(71) are not yet defined.
Automorphisms
An outer automorphism of L_{2}(71) of
order 2 may be obtained by mapping (a, b) to
(a, b^{ab2ababababab2ababab}).
The representations of L_{2}(71) available are:
 Some primitive permutation representations

Permutations on 72 points:
a and
b (GAP).
 Some matrix representations in characteristic 0:

Dimension 71 over Z:
a and b (GAP).

Dimension 72 over Z(z35) (monomial):
a and b (GAP).
The representations of 2.L_{2}(71) = SL_{2}(71) available are:
 Some matrix representations in characteristic 0:

Dimension 72 over Z(z70) (monomial):
A and B (GAP).
The representations of L_{2}(71):2 = PGL_{2}(71) available are:
The representations of 2.L_{2}(71):2 available are:
Maximal subgroups
The maximal subgroups of L_{2}(71) are as follows.

71:35, with generators
ab^{2}, abab^{2}abab^{2}abab^{2}ab^{2}ababab

D_{72}, with generators
a, a^{ababab}

D_{70}, with generators
a, a^{ab}

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

A_{5}, with standard generators
a, b^{ab2ab2}

S_{4}, with generators
a, b^{ab2abababababab}

S_{4}, with generators
a, b^{abab2ab2ab2ab2ab2ab2}
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Version 2.0 created on 28th April 2004.
Last updated 30.04.04 by SN.