ATLAS: Orthogonal group O8-(2)

Order = 197406720.
Mult = 1.
Out = 2.
See also ATLAS of Finite Groups, pp88-89.

The following information is available for O8-(2):

Standard generators

Standard generators of O8-(2) are a and b where a is in class 2C, b is in class 3C and ab has order 17, ababb has order 17, and abababb has order 30.

Standard generators of O8-(2):2 are c and d where c is in class 2D, d has order 14, and cd has order 17, and cdcdd has order 12.

Representations

The representations of O8-(2) available are
• Some primitive permutation representations.
• Some irreducible representations in characteristic 2.
• Some irreducible representations in characteristic 3.
• Some irreducible representations in characteristic 5.
• Some irreducible representations in characteristic 7.
• Some irreducible representations in characteristic 17.
• Some faithful irreducibles in characteristic 0
• Dimension 34 over Z: a and b (GAP).
• Dimension 51 over Z: a and b (GAP).
• Dimension 84 over Z: a and b (GAP).
• Dimension 204[b] over Z: a and b (GAP).
The representations of O8-(2):2 available are

Maximal subgroups

The maximal subgroups of O8-(2) are as follows.
• 2^6:U4(2)
• S6(2)
• 2^(3+6):(L3(2) x 3)
• 2^(1+8):(S3 x A5)
• (3 x A8):2
• L2(16):2
• (S3 x S3 x A5):2
• L2(7)
The maximal subgroups of O8-(2):2 are as follows.
• O8-(2)
• 2^6:U4(2):2
• S6(2) x 2
• 2^(3+6):(L3(2) x S3)
• 2^(1+8):(S3 x S5)
• S3 x S8
• L2(16):4
• (S3 x S3):2 x S5
• L2(7):2

Conjugacy classes

A set of generators for the maximal cyclic subgroups of O8-(2) can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements. These classes are compatible with the Atlas of Brauer Characters. A set of generators for the maximal cyclic subgroups of O8-(2):2 can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements. These classes are compatible with the Atlas of Brauer Characters.

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 program syntax
Word programs applied
All necessary standard generators are defined26.01.01RAW
All representations are in standard generators

Go to main ATLAS (version 2.0) page.
Go to classical groups page.
Go to old O8-(2) page - ATLAS version 1.
Anonymous ftp access is also available on for.mat.bham.ac.uk, user atlasftp, password atlasftp. Files can be found in directory v2.0 and subdirectories.

Version 2.0 created on 25th January 2001.
Last updated 04.03.04 by SJN.
Information checked to Level 0 on 25.01.01 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.