ATLAS: Unitary group U3(3), Derived group G2(2)'

Order = 6048 = 25.33.7.
Mult = 1.
Out = 2.

Standard generators

Standard generators of U3(3) are a and b where a has order 2, b has order 6 and ab has order 7.

Standard generators of U3(3):2 = G2(2) are c and d where c is in class 2B, d is in class 4D and cd has order 7.


Presentations of U3(3) and U3(3):2 = G2(2) on their standard generators are given below.

< a, b | a2 = b6 = (ab)7 = [a, (ab2)3] = b3[b2, ab3a]2 = 1 >.

< c, d | c2 = d4 = (cd)7 = [c, d]6 = (cd(cd2)3)2 = [d2, cdc]3 = 1 >.


The representations of U3(3) available are: The representations of U3(3):2 = G2(2) available are:

Maximal subgroups

The maximal subgroups of U3(3) are as follows. The maximal subgroups of U3(3):2 = G2(2) are as follows.

Conjugacy classes

At the moment, we are only going to give enough class representatives so that we can sort out some of our generality problems.

Representatives of some of the 14 conjugacy classes of U3(3) are given below.

Representatives of some of the 16 conjugacy classes of U3(3):2 are given below.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old U3(3) page Go to old U3(3) page - ATLAS version 1.
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Version 2.0 created on 19th July 2000.
Last updated 03.03.04 by SJN.
Information checked to Level 0 on 19.07.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.