ATLAS: Orthogonal group O_{10}^{}(2)
Order = 25015379558400 = 2^{20}.3^{6}.5^{2}.7.11.17.
Mult = 1.
Out = 2.
The following information is available for O_{10}^{}(2):
Standard generators of O_{10}^{}(2) are a and
b, where a is in class 2A, d is in class 5B, ab
has order 33 and abababb has order 18. The last condition is
equivalent to: ababbbb has order 3.
Standard generators of O_{10}^{}(2):2 are c and
d, where c is in class 2E, d has order 11 and cd
has order 36.
N.B. The old generators for 010(2):2 that were here before 20.11.97 are no longer available.
The representations of O_{10}^{}(2) available are:

Permutations on 495 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 528 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 10 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 16 over GF(4):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 16 over GF(4):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 44 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 100 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 164 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 670 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of O_{10}^{}(2):2 available are:

Permutations on 495 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 528 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 104448 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP),
c and d (Magma).

Dimension 10 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 32 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 44 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 100 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 164 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 670 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
The maximal subgroups of O_{10}^{−}(2) are as follows.
The maximal subgroups of O_{10}^{−}(2):2 are as follows.
A set of generators for the maximal cyclic subgroups of O_{10}^{}(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 O_{10}^{}(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.
Check  Date  By whom  Remarks 
Links work (except representations)    
Links to (meataxe) representations work and have right degree and field   
All info from v1 is included   
HTML page standard   
Word program syntax   
Word programs applied   
All necessary standard generators are defined  26.01.01  RAW 
All representations are in standard generators  
Go to main ATLAS (version 2.0) page.
Go to classical groups page.
Go to old O10(2) page  ATLAS version 1.
Anonymous ftp access is also available.
See here for details.
Version 2.0 created on 26th January 2001.
Last updated 29.11.01 by JNB.
Information checked to
Level 0 on 26.01.01 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.