ATLAS: Orthogonal group O9(3)
Order = 65784756654489600 = 214.316.52.7.13.41.
Mult = 2.
Out = 2.
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:
-
Dimension 9 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of 2.O9(3) available are:
-
Dimension 16 over GF(3):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
The representations of O9(3):2 available are:
-
Dimension 9 over GF(3):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
The representations of 2.O9(3):2 [with O(C) = 4] available are:
-
Dimension 16 over GF(3):
C and
D (Meataxe),
C and
D (Meataxe binary),
C and
D (GAP).
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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.