ATLAS: Unitary group U4(2), Symplectic group S4(3)

Order = 25920 = 26.34.5.
Mult = 2.
Out = 2.

The following information is available for U4(2):


Standard generators

Standard generators of U4(2) = S4(3) are a and b, where a in class 2A and b has order 5 and ab has order 9.
Standard generators of the double cover 2.U4(2) = Sp4(3) are preimages A and B where B has order 5 and AB has order 9.

Standard generators of U4(2):2 = S4(3):2 are c and d, where c in class 2C and d has order 9 and cd has order 10.
Standard generators of either of the double covers 2.U4(2):2 are preimages C and D where D has order 9.


Automorphisms

An outer automorphism of U4(2) of order 2 may be obtained by mapping (a, b) to (a, bbbb).

Presentations

Presentations of U4(2) and U4(2):2 in terms of their standard generators are given below.

< a, b | a2 = b5 = (ab)9 = [a, b]3 = [a, bab]2 = 1 >.

< c, d | c2 = d9 = (cd2)8 = [c, d2]2 = [c, d3cd3] = 1 >.


Representations

The representations of U4(2) available are:
These representations are ordered [supposedly] with respect to ab being in class 9A. The representations of 2.U4(2) available are: The representations of U4(2):2 available are:
The representations of 2.U4(2):2 (ATLAS-version) available are:

Maximal subgroups

The maximal subgroups of U4(2) are as follows. The maximal subgroups of U4(2):2 are as follows.

Conjugacy classes

A set of generators for the maximal cyclic subgroups of U4(2) can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements.

A set of generators for the maximal cyclic subgroups of U4(2).2 can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements.


Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old U4(2) page Go to old U4(2) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 25th July 2000.
Last updated 16.12.04 by JNB.
Information checked to Level 0 on 25.07.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.