ATLAS: Linear group L_{2}(81)
Order = 265680 = 2^{4}.3^{4}.5.41.
Mult = 2.
Out = 4 × 2.
The following information is available for L_{2}(81):
Standard generators
Standard generators of L_{2}(81) are a
and b where
a has order 2,
b has order 3,
ab has order ??
and ababb has order ??.
Representations
The representations of L_{2}(81) available are:
- a and
b as
permutations on 82 points.
- a and
b as
3 × 3 matrices over GF(81) - the natural representation as O3(81).
Maximal subgroups
The maximal subgroups of L_{2}(81) are as follows.
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Last updated 18th March 1998,
R.A.Wilson, R.A.Parker and J.N.Bray