ATLAS: Linear group L_{3}(8)
Order = 16482816 = 2^{9}.3^{2}.7^{2}.73.
Mult = 1.
Out = 6.
Standard generators
Standard generators of L_{3}(8) are a and b where
a has order 2, b has order 3 and ab has order 21.
Standard generators of L_{3}(8):2 are
c
and d where
c is in class ,
d is in class ,
and cd is in class
Standard generators of L_{3}(8):3 are e and f where
e has order 2, f has order 6, ef has order 9, efff
has order 3 and efeffefffff has order 21. These conditions distinguish
classes 6B and 6B'. [NB: Class 6A is not in L_{3}(8):3.]
Standard generators of L_{3}(8):6 are
g
and h where
g is in class ,
h is in class ,
and gh is in class
Representations
The representations of L_{3}(8) available are
- a and
b as
permutations on 73 points.
- a and
b as
permutations on 73 points.
- a and
b as
3 × 3 matrices over GF(8) - the natural representation - changed to standard generators on 9/11/98.
The representations of L_{3}(8):3 available are
- e and
f as
permutations on 73 points.
- e and
f as
permutations on 73 points.
- e and
f as
9 × 9 matrices over GF(2) - changed to standard generators on 10/11/98.
- e and
f as
9 × 9 matrices over GF(2).
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Last updated 10th November 1998,
R.A.Wilson, R.A.Parker and J.N.Bray