ATLAS: Symplectic group S8(3)
Order = 65784756654489600 = 214.316.52.7.13.41.
Mult = 2.
Out = 2.
The following information is available for S8(3):
Standard generators of S8(3) are a and b where
a is in class 2B, b is in class 4D and ab has order 14.
Standard generators of the double cover 2.S8(3) = Sp8(3)
are preimages A and B such that AB3(AB)4 has order 9.
Standard generators of S8(3):2 are not defined.
Standard generators of either of the double covers 2.S8(3):2 are not defined.
To find standard generators of S8(3):
- Find an element x in class 2B, say by powering up an element
of order 24, 72 or 90.
- Find an element t in class 4D, say by powering up an element
of order 84.
- Find a conjugate y of t such that xy has order 14.
- The elements x and y are standard generators.
The representations of S8(3) available are:
-
Some primitive permutation representations.
-
Permutations on 3280 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
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Version 2.0 file created on 4th August 2004.
Last updated 4.8.04 by SJN.