ATLAS: Orthogonal group O9(3)

Order = 65784756654489600 = 214.316.
Mult = 2.
Out = 2.

Standard generators

Standard generators of O9(3) are a and b where a is in class 2A, b is in class 9N/O, ab has order 41 and ababb has order 39.
Standard generators of the double cover 2.O9(3) are preimages A and B where B has order 9 and AB has order 41.

Standard generators of O9(3):2 are c and d where c has order 2E, d is in class 9NO, cd has order 84 and cdcdd has order 12.
Standard generators of either double cover 2.O9(3):2 are preimages C and D where D has order 9.

NB 1: The generators for [2.]O9(3):2 in v1 and v2.0 are identical, but the generators for O9(3) in v1 and v2.0 differ despite the fact that the v1­generators are (2, 9, 41)­generators - the involution is in the wrong class.

NB 2: Classes 2A and 2E are the classes of negated reflections. Classes 9N/O are the elements of order 9 whose centraliser order in both O9(3) and O9(3):2 is 81.


The representations of O9(3) available are: The representations of 2.O9(3) available are: The representations of O9(3):2 available are: The representations of 2.O9(3):2 [with O(C) = 4] available are:

Maximal subgroups

Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old O9(3) page Go to old O9(3) page - ATLAS version 1.
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Version 2.0 created on 24th August 2000.
Last updated 17.10.00 by JNB.
Information checked to Level 0 on 24.08.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.