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

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.

Black box algorithms

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.

Representations

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).

Go to main ATLAS (version 2.0) page.
Go to classical groups page.
Anonymous ftp access is also available. See here for details.

Version 2.0 file created on 4th August 2004.
Last updated 4.8.04 by SJN.