ATLAS: Orthogonal group O10+(2)

Order = 23499295948800 =
Mult = 1.
Out = 2.

The following information is available for O10+(2):

Standard generators

Standard generators of O10+(2) are a and b where a is in class 2A, b is in class 20A and ab has order 21.
Standard generators of O10+(2):2 are c and d where c is in class 2E, d has order 16 and cd has order 45.


An outer automorphism of O10+(2) can be taken to map (a, b) to (a, b-1).

Black box algorithms

To find standard generators for O10+(2): To find standard generators for O10+(2).2:


Presentations of O10+(2) and O10+(2):2 on their standard generators are given below:

< a, b | a2 = b20 = (ab)21 = (ab2)17 = . . . = 1 >.

< c, d | c2 = d16 = (cd)45 = [c, d]3 = [c, d2]2 = [c, d3]3 = [c, d4]2 = [c, d5]2 = [c, d6]2 = [c, d7]2 = (cd8)4 = (cd2cd2cd-1)9 = 1 >.

The relations (cd)45 = [c, d]3 = 1 in the O10+(2):2 presentation are redundant.
These presentations are available in Magma format as follows: O10+(2):2 on c and d.


The representations of O10+(2) available are: The representations of O10+(2):2 available are:

Maximal subgroups

The maximal subgroups of O10+(2) are as follows. The maximal subgroups of O10+(2):2 are as follows.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old O10+(2) page Go to old O10+(2) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 23rd January 2004.
Last updated 26.01.04 by JNB/SJN.
Information checked to Level 0 on 13.10.03 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.