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

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 >.


Representations

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.
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Last updated 1st December 1998,
R.A.Wilson, R.A.Parker and J.N.Bray