ATLAS: Unitary group U7(2)

Order = 227787103272960 = 221.38.5.7.11.43.
Mult = 1.
Out = 2.
The page for the group 214.U7(2) (non­split extension) is available here.

The following information is available for U7(2):


Standard generators

Standard generators of U7(2) are a and b where a is in class 2A, b has order 7, ab has order 33 and abb has order 45.

NB: Class 2A is the class of transvections of U7(2).


Automorphisms

An outer automorphism of U7(2) may be obtained by mapping (a, b) to (a, b-1).

Presentation

A presentation of U7(2) on its standard generators is given below.

< a, b | a2 = b7 = (ab)33 = [a, b]3 = [a, b2]3 = [a, b3]3 = [a, bab]2 = [a, b2ab2]2 = [a, bab2]3 = (abab-3ab-3)8 = 1 >.

This presentation is available in Magma format as follows: U7(2) on a and b.


Representations

The representations of U7(2) available are:

Maximal subgroups

The maximal subgroups of U7(2) are as follows [from Kleidman's list]:
Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 8th December 1999.
Last updated 02.08.00 by JNB.
Information checked to Level 0 on 09.12.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.