ATLAS: Orthogonal group O8-(2)
Order = 197406720.
Mult = 1.
Out = 2.
Standard generators
Standard generators of O8-(2) are
a
and b where
a is in class 2C,
b is in class 3C
and ab has order 17,
ababb has order 17,
and abababb has order 30.
(These are not ideal, but they have been on this page for a year,
so I don't want to change them unless absolutely necessary.)
Standard generators of O8-(2):2 are
c
and d where
c is in class 2D,
d has order 14,
and cd has order 17,
and cdcdd has order 12.
N.B. The old generators for O8-(2):2, here before
19.02.97, are no longer available.
Representations
The representations of O8-(2) available are
- Some irreducible representations in characteristic 2.
- a and
b as
8 x 8 matrices over GF(2) - the natural representation.
- a and
b as
8 x 8 matrices over GF(4).
- a and
b as
26 x 26 matrices over GF(2).
- a and
b as
48 x 48 matrices over GF(2).
- a and
b as
48 x 48 matrices over GF(4).
- Some irreducible representations in characteristic 3.
- a and
b as
34 x 34 matrices over GF(3).
- a and
b as
50 x 50 matrices over GF(3).
- Some irreducible representations in characteristic 5.
- a and
b as
34 x 34 matrices over GF(5).
- a and
b as
51 x 51 matrices over GF(5).
- a and
b as
84 x 84 matrices over GF(5).
- Some irreducible representations in characteristic 7.
- a and
b as
33 x 33 matrices over GF(7).
- a and
b as
51 x 51 matrices over GF(7).
- a and
b as
84 x 84 matrices over GF(7).
- Some irreducible representations in characteristic 17.
- a and
b as
34 x 34 matrices over GF(17).
- a and
b as
51 x 51 matrices over GF(17).
- a and
b as
83 x 83 matrices over GF(17).
- Some primitive permutation representations.
- a and
b as
permutations on 119 points.
- a and
b as
permutations on 136 points.
- a and
b as
permutations on 765 points.
- a and
b as
permutations on 1071 points.
- a and
b as
permutations on 1632 points.
- a and
b as
permutations on 24192 points.
- a and
b as
permutations on 45696 points.
The representations of O8-(2):2 available are
- c and
d as
8 x 8 matrices over GF(2) - the natural representation.
- c and
d as
34 x 34 matrices over GF(3).
- c and
d as
50 x 50 matrices over GF(3).
- c and
d as
permutations on 119 points.
Maximal subgroups
The maximal subgroups of O8-(2) are as follows.
The maximal subgroups of O8-(2):2 are as follows.
Return to main ATLAS page.
Last updated 24.03.99
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk