ATLAS: Linear group L_{2}(73)
Order = 194472 = 2^{3}.3^{2}.37.73.
Mult = 2.
Out = 2.
The following information is available for L_{2}(73):
Standard generators of L_{2}(73) are a of
order 2, b of order 3 such that ab has order 73.
Standard generators of the double cover
2.L_{2}(73) = SL_{2}(73) are preimages
A and B such that B has order 3 and
AB has order 73.
Standard generators of L_{2}(73):2 = PGL_{2}(73) are not yet defined.
Standard generators of the double cover 2.L_{2}(73):2 = 2.PGL_{2}(73) are not yet defined.
Automorphisms
An outer automorphism of L_{2}(73) of
order 2 may be obtained by mapping (a, b) to
(a, b^{ab2ab2abababababab}).
The representations of L_{2}(73) available are:
 Some primitive permutation representations

Permutations on 74 points:
a and
b (GAP).
 Some matrix representations in characteristic 0:

Dimension 73 over Z:
a and b (GAP).

Dimension 74 over Z(z36) (monomial):
a and b (GAP).
The representations of 2.L_{2}(73) = SL_{2}(73) available are:
 Some matrix representations in characteristic 0:

Dimension 74 over Z(z72) (monomial):
A and B (GAP).
The representations of L_{2}(73):2 = PGL_{2}(73) available are:
The representations of 2.L_{2}(73):2 available are:
Maximal subgroups
The maximal subgroups of L_{2}(73) are as follows.

73:36, with generators
a, ababab^{2}ab^{2}ababab

D_{74}, with generators
a, a^{ab}

D_{72}, with generators
a, a^{ab2abab}

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

S_{4}, with generators
a, b^{abab2abab2ab}
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Version 2.0 created on 28th April 2004.
Last updated 30.04.04 by SN.