ATLAS: Unitary group U5(3)

Order = 258190571520 = 211.310.5.7.61.
Mult = 1.
Out = 2.
The page for the group 310.U5(3) (non­split extension) is available here.

The following information is available for U5(3):


Standard generators

Standard generators for U5(3) are a and b where a is in class 3A, b has order 5 and ab has order 16.
Standard generators for U5(3):2 are c and d where c is in class ??, d has order ? and cd has order ??.

NB: Class 3A is the class of transvections in U5(3).

Automorphisms

An [outer] automorphism of U5(3) of order 2 can be obtained by mapping (a, b) to (a-1, b).

Presentations

< a, b | a3 = b5 = [a, bab-1ab] = [a, b-2ab2] = (babababa-1)4 = (ababa-1bab2)5 = 1 >.

Representations

The representations of U5(3) available are:

Maximal subgroups

The maximal subgroups of U5(3) are (I reckon) as follows [implementation of word programs not checked]:
Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old U5(3) page There is no old U5(3) page in the ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 24th September 2001.
Last updated 24.09.01 by JNB.
Information checked to Level 0 on 24.09.01 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.