ATLAS: Unitary group U3(4)

Order = 62400 = 26.3.52.13.
Mult = 1.
Out = 4.

Standard generators

Standard generators of U3(4) are a and b where a has order 2, b has order 3 and ab has order 13.
A generating outer automorphism may be obtained by mapping (a, b) to ((ab)^-2a(ab)^2, (abb)^-5b(abb)^5).

Standard generators of U3(4):2 are c and d where c has order 2, d has order 3, cd has order 8, cdcdd has order 13 and cdcdcdcddcdcddcdd has order 10.
NB: Of course, c is in class 2B.

Standard generators of U3(4):4 are e and f where e is in class 2A, f is in class 4B or 4B', ef has order 12 and efefffeff has order 6.
NB: These conditions distinguish between classes 4B and 4B'. Classes 4B and 4B' are the classes for which the ATLAS class 4B is proxy.


Presentations

< a, b | a2 = b3 = (ab)13 = [a, b]5 = [a, babab]3 = 1 >.

< c, d | c2 = d3 = (cd)8 = [c, d]13 = [c, dcdcdcd-1cdcd]2 = [c, d-1cdcd]5 = 1 >.

< e, f | e2 = f4 = (ef)12 = [e, f]5 = (ef2)10 = efefef2efef2ef-1ef2efefef-1ef2ef-1ef2 = 1 >.


Representations

The representations of U3(4) available are The representations of U3(4):2 available are The representations of U3(4):4 available are
NB: Changed to standard generators on 26.05.98.

Maximal subgroups

The maximal subgroups of U3(4) are as follows. The maximal subgroups of U3(4):2 are as follows. The maximal subgroups of U3(4):4 are as follows.
Return to main ATLAS page. Last updated 12.04.00

- R.A.Wilson@bham.ac.uk
- richard@ukonline.co.uk