ATLAS: Orthogonal group O8-(3)

Order = 10151968619520 = 210.312.5.7.13.41.
Mult = 2.
Out = 2 × 2.

The following information is available for O8-(3):


Standard generators

Standard generators of O8-(3) are a and b where a is in class 2A, b is in class 4F, ab has order 41, abb has order 6 and ababb has order 41.
Standard generators of the double cover 2.O8-(3) are preimages A and B where AB has order 41 and ABABB has order 41.

Standard generators of O8-(3):21 are c and d where c is in class 2D/E, d is in class 8F, cd has order 41, cdd has order 12 and cdcdd has order 18.
We may obtain d as d = cx, where x has order 41, cx has order 8, cxx has order 12 and cxxx has order 18.
Standard generators of the double cover 2.O8-(3):21 are preimages C and D where C has order 2 and CD has order 41.

Type I standard generators of O8-(3).23 are g and h where g is in class 3A, h is in class 8V/W, gh has order 56 and ghh has order 36.
Type II standard generators of O8-(3).23 are g2 and h2 where g2 is in class 2A, h2 is in class 8X/Y, g2h2 has order 24, g2h2h2 has order 7, g2h2h2h2 has order 56 and g2h2h2h2h2 has order 3.

Standard generators of O8-(3).22 are i and j where j is in class 2DE, j is in class 8B1, ij has order 82 and ijj has order 8.
We may obtain j as j = ix, where x has order 82, ix has order 8 and ixx has order 8.

Note 1: Some class definitions are here.
Note 2: SO8-(3) = O8-(3) × 2 and GO8-(3) = O8-(3):21 × 2.
Note 3: There are no double covers of O8-(3).23 and O8-(3).22 [that contain 2.O8-(3)].
Note 4: No standard generators were defined in v1. Any representations in v1 will be on different generators.


Representations

The representations of O8-(3) available are: The representations of 2.O8-(3) available are: The representations of O8-(3):21 available are: The representations of 2.O8-(3):21 available are: The representations of O8-(3).23 available are: The representations of O8-(3).22 available are:

Maximal subgroups

The maximal subgroups of O8-(3) are as follows - INCOMPLETE: The maximal subgroups of O8-(3):21 are as follows - INCOMPLETE: The maximal subgroups of O8-(3):22 are as follows - INCOMPLETE: The maximal subgroups of O8-(3).23 are as follows - INCOMPLETE: The maximal subgroups of O8-(3).22 are as follows - INCOMPLETE:

Note: The L2(81) normalisers have abstract specification C(2H). The outer automorphisms of L2(81):21 and L2(81):41 are field automorphisms; this is for consistency with the GAP tables.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old O8-(3) page Go to old O8-(3) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 24th August 2000.
Last updated 23.02.04 by JNB.
Information checked to Level 0 on 24.08.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.