# ATLAS: Lyons group Ly

Order = 51765179004000000 = 28.37.56.7.11.31.37.67.
Mult = 1.
Out = 1.

### Standard generators

Standard generators of the Lyons group Ly are a and b where a has order 2, b is in class 5A, ab has order 14 and abababb has order 67.

### Black box algorithms

To find standard generators for Ly:
• Find any element x of order 2 by taking a suitable power of any element of even order.
• Find any element of order 20, 25 or 40. This powers up to a 5A­element, y say.
• Find a conjugate a of x and a conjugate b of y, whose product has order 14, such that abababb has order 67.

### Representations

The representations of Ly available are:
• a and b as 2480 × 2480 matrices over GF(4).
• a and b as 651 × 651 matrices over GF(3).
• a and b as 111 × 111 matrices over GF(5).
• a and b as 517 × 517 matrices over GF(5) - kindly provided by K. Lux.

### Maximal subgroups

The maximal subgroups of Ly 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 24.09.99

R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk
jnb@for.mat.bham.ac.uk