ATLAS: Linear group L3(5)
Order = 372000.
Mult = 1.
Out = 2.
Standard generators
Standard generators of L3(5) are
a
and b where
a has order 3,
b is in class 5A,
ab has order 20.
Representations
The representations of L3(5) available are
- a and
b as
3 x 3 matrices over GF(5) - the natural representation.
- a and
b as
permutations on 31 points.
The representations of L3(5):2 available are
Maximal subgroups
The maximal subgroups of L3(5) are as follows.
- 5^2:GL2(5).
- 5^2:GL2(5).
- S5.
- 4^2:S3.
- 31:3.
The maximal subgroups of L3(5):2 are as follows.
- L3(5).
- 5^1+2.[2^5].
- GL_2(5).2
- S5 x2.
- 4^2:D12.
- 31:6.
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Last updated 18.03.96
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk