ATLAS: Linear group L_{3}(11)
Order = 212427600 = 2^{4}.3.5^{2}.7.11^{3}.19.
Mult = 1.
Out = 2.
Standard generators
Standard generators of L_{3}(11) are a and
b where a has order 3,
b is in class 11A,
ab has order 120, abb has order 10 and ababb has order 40. The last two conditions can be replaced by ab^{5} has order 55.
NB: Class 11A is the class of transvections in the natural representation of L_{3}(11).
Standard generators of L_{3}(11):2 are not defined.
Representations
The representations of L_{3}(11) available are
- a and
b as
permutations on 133 points.
- a and
b as
3 × 3 matrices over GF(11) - the natural representation.
The representations of L_{3}(11):2 available are
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Last updated 13.12.97
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk