ATLAS: Unitary group U3(5)

Order = 126000.
Mult = 3.
Out = S3.

Standard generators

Standard generators of U3(5) are a and b where a has order 3, b is in class 5A, and ab has order 7.
Standard generators of 3.U3(5) are pre-images A and B where B has order 5, and AB has order 7.
Standard generators of U3(5):2 are c and d where c is in class 2B, d is in class 4A, cd has order 10, and cdcdddcdd has order 2.
Standard generators of 3.U3(5):2 are pre-images C and D where D has order 4.

Representations

The representations of U3(5) available are The representations of U3(5):2 available are The representations of 3.U3(5) available are The representations of 3.U3(5):2 available are

Maximal subgroups

The maximal subgroups of U3(5) are as follows. The maximal subgroups of U3(5):2 are as follows. The maximal subgroups of U3(5):3 are as follows. The maximal subgroups of U3(5):S3 are as follows.

Conjugacy classes

A set of generators for the maximal cyclic subgroups can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements. Problems of algebraic conjugacy have been dealt with.
We have made a choice of the cyclic ordering of classes 5B/C/D, which may change if we ever decide on a consistent convention for such things.
- Return to main ATLAS page. - Last updated 12.04.00

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