ATLAS: Linear group L_{2}(27)
Order = 9828 = 2^{2}.3^{3}.7.13.
Mult = 2.
Out = 6.
Standard generators
Standard generators of L_{2}(27) are a
and b where
a has order 2, b has order 3 and ab has order 7.
Standard generators of the double cover 2.L_{2}(27) = SL_{2}(27) are preimages A and B where
B has order 3
and AB has order 7.
Representations
The representations of L_{2}(27) available are
- a and
b as
permutations on 28 points.
- a and
b as
3 × 3 matrices over GF(27).
The representation of 2.L_{2}(27) available is
- A and
B as
2 × 2 matrices over GF(27).
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Last updated 06.12.97
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk