ATLAS: Orthogonal group O8+(2)

Order = 174182400 = 212.35.52.7.
Mult = 2 2.
Out = S3.

Standard generators

Standard generators of O8+(2) are a and b where a is in class 2E, b is in class 5A, ab is in class 12F (or 12G) and ababababbababbabb has order 8.
[Actually, b is allowed to be in classes 5B or 5C as they are automorphic to class 5A, but then you must change the class you allow ab to belong to. To ensure that ab is in the correct class relative to the class of b, we just need to check that abb has order 15.]
Standard generators of the double cover 2.O8+(2) are preimages A and B where B has order 5, ABB has order 15 and B is in class +5A.
[In 2.O8+(2), class +5A is not automorphic to classes +5B or +5C. A condition equivalent to B being in class +5A is that ABABB has order 15.]
Standard generators of 22.O8+(2) are preimages A and B where B has order 5 and ABB has order 15.

Standard generators of O8+(2):2 are c and d where c is in class 2F, d is in class 10BC and cd has order 18.
[If you can't distinguish class 10BC from class 10A, then also add the condition that cdd has order 30.]
Standard generators of any 2.O8+(2).2 are preimages C and D where CD(CD4)3 has order 3.


Representations

The representations of O8+(2) available are The representation of 2.O8+(2) available is The representation of 2.O8+(2):2 available is The representation of 2^2.O8+(2):3 available is The representation of 2^2.O8+(2):S3 available is
- Return to main ATLAS page. - Last updated 25.08.99

- R.A.Wilson@bham.ac.uk
- richard@ukonline.co.uk