ATLAS: Linear group L_{2}(97)
Order = 456288 = 2^{5}.3.7^{2}.97.
Mult = 2.
Out = 2.
The following information is available for L_{2}(97):
Standard generators of L_{2}(97) are a of
order 2, b of order 3 such that ab has order 97.
Standard generators of the double cover
2.L_{2}(97) = SL_{2}(97) are preimages
A and B such that B has order 3 and
AB has order 97.
Standard generators of L_{2}(97):2 = PGL_{2}(97) are not yet defined.
Standard generators of the double cover 2.L_{2}(97):2 = 2.PGL_{2}(97) are not yet defined.
Automorphisms
An outer automorphism of L_{2}(97) of
order 2 may be obtained by mapping (a, b) to
(a, b^{abab2ab2abababab}).
The representations of L_{2}(97) available are:
 Some primitive permutation representations

Permutations on 98 points:
a and
b (GAP).
 Some matrix representations in characteristic 0:

Dimension 97 over Z:
a and b (GAP).

Dimension 98 over Z(z48) (monomial):
a and b (GAP).
The representations of 2.L_{2}(97) = SL_{2}(97) available are:
 Some matrix representations in characteristic 0:

Dimension 98 over Z(z96) (monomial):
A and B (GAP).
The representations of L_{2}(97):2 = PGL_{2}(97) available are:
The representations of 2.L_{2}(97):2 available are:
Maximal subgroups
The maximal subgroups of L_{2}(97) are as follows.

97:48, with generators
a, ababab^{2}ab^{2}ababab^{2}abab

D_{98}, with generators
a, a^{ab}

D_{96}, with generators
a, a^{ab2abab}

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

S_{4}, with generators
a, b^{ab2ab2ababababab}
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Version 2.0 created on 28th April 2004.
Last updated 30.04.04 by SN.