ATLAS: Orthogonal group O9(3)
Order =65784756654489600.
Mult = 2.
Out = 2.
Standard generators
Standard generators of O9(3) are not defined. The present generators are
a
and b where
a has order 2,
b has order 9,
ab has order 41,
and abb has order.
Standard generators of the double cover 2.O9(3) are pre-images
A
and B where
A has order
and AB has order .
Standard generators of O9(3):2 are
c
and d where
c has order ,
d is in class ,
and cd has order .
Standard generators of the double cover 2.O9(3):2 are pre-images
C
and D where
C has order
and CD has order .
Representations
The representation of O9(3) available is
- a and
b as
9 x 9 matrices over GF(3).
The representation of O9(3):2 available is
- c and
d as
9 x 9 matrices over GF(3).
The representation of 2.O9(3).2 available is
- C and
D as
16 x 16 matrices over GF(3).
Maximal subgroups
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Last updated 23.11.97
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk