ATLAS: O'Nan group ON

Order = 460815505920.
Mult = 3.
Out = 2.

Standard generators

Standard generators of the O'Nan group ON are a and b where a has order 2, b is in class 4A, and ab has order 11.
Standard generators of the triple cover 3ON are pre-images A and B where A has order 2, and B has order 4.
Standard generators of the automorphism group ON:2 are c and d where c is in class 2B, d is in class 4A, and cd has order 22.
Standard generators of 3ON:2 are preimages C and D, where D has order 4.
A pair of generators conjugate to a, b can be obtained as
a' = (cdd)^{-2}dd(cdd)^2, b' = d.

The outer automorphism of O'N may be realised by mapping (a,b) to (a,b-1).

Black box algorithms

To find standard generators for O'N: To find standard generators for O'N.2:

Representations

The representations of ON available are The representations of 3ON available are The representations of ON:2 available are The representations of 3ON:2 available are

Maximal subgroups

The maximal subgroups of O'N are The maximal subgroups of O'N: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 09.12.99

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