# 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.
• etc
The maximal subgroups of O8-(2):2 are as follows.
• O8-(2)
• etc