ATLAS: Suzuki group Suz

Order = 448345497600.
Mult = 6.
Out = 2.

Standard generators and automorphisms

Standard generators of the Suzuki group Suz are a and b where a is in class 2B, b is in class 3B, ab has order 13, and ababb has order 15.
Standard generators of 2.Suz are pre-images A and B where B has order 3 and AB has order 13.
Standard generators of 3.Suz are pre-images A and B where A has order 2 and AB has order 13.
Standard generators of 6.Suz are pre-images A and B where A has order 4, B has order 3 and AB has order 13.

Standard generators of the automorphism group Suz:2 are c and d where c is in class 2C, d is in class 3B, and cd has order 28.
Standard generators of 2.Suz:2 are pre-images C and D where D has order 3.
Standard generators of 3.Suz:2 are pre-images C and D where D is in class +3B (equivalently, CDCDD has order 7).

The outer automorphism of Suz may be realised by mapping a, b to (ab)^-2bab, (abb)^-2b(abb)^2.
If c' is the 15th power of this automorphism, and d' =b, then (c',d') is conjugate to (c,d).

Black box algorithms

To find standard generators for Suz: To find standard generators for Suz.2:

Representations

Representations are available for the following decorations of Suz: The representations of Suz available are The representations of 2.Suz available are The representations of 3.Suz available are The representations of 6.Suz available are The representations of Suz:2 available are The representations of 2.Suz:2 available are The representations of 3.Suz:2 available are The representations of 6.Suz:2 available are

Maximal subgroups

The maximal subgroups of Suz are The maximal subgroups of Suz:2 are

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 are not yet dealt with.
- Return to main ATLAS page. - Last updated 19.12.00

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