ATLAS: Exceptional group 3D4(3)

Order = 20560831566912 = 26.312.72.132.73.
Mult = 1.
Out = 3.

The following information is available for 3D4(3):

Standard generators

Standard generators of 3D4(3) are a and b where a is in class 3A, b is in class 13G/H (the ones with fixed points in the natural 8-dimensional representation), ab has order 73 and ababb has order 13.
(These conditions distinguish between classes 13G and 13H.)
Add the condition that abb has order 73 if you can't distinguish between 13G/H and 13I/J/K. Note that (3A, 13A/B/C/D/E/F, 73)-triples are impossible.
Standard generators of 3D4(2):3 are not yet defined.

Note that elements of orders 42, 78, 84 power up to 3A. Nothing properly powers up to 13G/H or 13I/J/K. These classes contain 5/169 elements of the group, and 2/169 of the group is in class 13G/H. 13A/B/C/D/E/F has centraliser 13 × L3(3), so obtaining such elements without powering up is extremely unlikely.


The representations of 3D4(3) available are:

Maximal subgroups

The maximal subgroups of 3D4(3) are:

Conjugacy classes

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

Version 2.0 created on 10th October 2000.
Last updated 11.11.08 by JNB.
Information checked to Level 0 on 10.10.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.