ATLAS: Orthogonal group O7(3)

Order = 4585351680 = 29.39.5.7.13.
Mult = 6.
Out = 2.

The following information is available for O7(3):


Standard generators

Standard generators of O7(3) are a and b where a is in class 2A, b has order 7, ab has order 13 and abb has order 20.
Standard generators of the double cover 2.O7(3) are preimages A and B where B has order 7 and AB has order 13.
Standard generators of the triple cover 3.O7(3) are preimages A and B where A has order 2 and B has order 7.
Standard generators of the sextuple cover 6.O7(3) are preimages A and B where A has order 4, B has order 7, and AB has order 39.

Standard generators of O7(3):2 are c and d where c is in class 2D, d has order 7, and cd has order 26, and cdcdd has order 14.
Standard generators of the double cover 2.O7(3):2 are preimages C and D where D has order 7.
Standard generators of the triple cover 3O7(3):2 are preimages C and D where D has order 7.
Standard generators of the sixfold cover 6.O7(3):2 are preimages C and D where D has order 7.


Automorphisms

The outer automorphism of O7(3) may be realised by mapping (a, b) to (a, b-1). This automorphism resides in Class 2F.

Black box algorithms

To find standard generators for O7(3): To find standard generators for O7(3).2:

Representations

The representations of O7(3) available are The representations of 2.O7(3) available are The representation of 3.O7(3) available is The representations of O7(3):2 available are The representation of 2.O7(3).2 available is The representation of 3.O7(3):2 available is

Maximal subgroups

The maximal subgroups of O7(3) are as follows. The maximal subgroups of O7(3):2 are as follows.

Checks applied

CheckDateBy whomRemarks
Links work (except representations)
Links to (meataxe) representations work and have right degree and field
All info from v1 is included
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Word programs applied
All necessary standard generators are defined24.01.01RAW
All representations are in standard generators

Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old O7(3) page Go to old O7(3) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 24th January 2001.
Last updated 25.01.01 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.