ATLAS: Linear group L3(8)

Order = 16482816 = 29.32.72.73.
Mult = 1.
Out = 6.

The following information is available for L3(8):


Standard generators

Standard generators of L3(8) are a and b where a has order 2, b has order 3 and ab has order 21.

Standard generators of L3(8).2 are c and d where c is in class 2B, d has order 3, cd has order 8, cdcdd has order 63 and cdcdcdd has order 8.

Standard generators of L3(8).3 are e and f where e has order 2, f has order 12, ef has order 21, efeff has order 7, efefeff has order 12, efefefeff has order 12 and efefeffefeffeffeff has order 9.

Standard generators of L3(8).6 are g and h where g is in class 2A, h is in class 18D, gh has order 24, ghghh has order 14, ghghghh has order 3 and ghghghghghhghghhghh has order 6.


Automorphisms

An automorphism of L3(8) of order 2 may be obtained by mapping (a,b) to (a,b-1).

An automorphism of L3(8) of order 3 may be obtained by applying this program to the standard generators.

An automorphism of L3(8) of order 6 may be obtained by applying this program to the standard generators.


Black box algorithms

To find standard generators for L3(8): To find standard generators for L3(8).2: To find standard generators for L3(8).3: To find standard generators for L3(8).6:

Representations

The representations of L3(8) available are The representations of L3(8).2 available are The representationsof L3(8).3 available are: The representations of L3(8).6 available are

Maximal Subgroups

The maximal subgroups of L3(8) are as follows.

The maximal subgroups of L3(8).2 are as follows.

The maximal subgroups of L3(8).3 are as follows.

The maximal subgroups of L3(8).6 are as follows.


Conjugacy Classes

A set of generators for the maximal cyclic subgroups of L3(8) 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 L3(8).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 L3(8).3 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 L3(8).6 can be obtained by running this program on the standard generators. All conjugacy classes can therefore be found as suitable powers of these elements.


Main ATLAS page Go to main ATLAS (version 2.0) page.
Linear groups page Go to linear groups page.

Version 2.0 created on 10th February 2004.
Last updated 17.08.04 by RAA.
Information checked to Level 0 on 26.02.04 by RAA.
R.A.Wilson, R.A.Parker and J.N.Bray.