ATLAS: Alternating group A8, Linear group L4(2)

Order = 20160 =
Mult = 2.
Out = 2.
See also ATLAS of Finite Groups, p22.

Standard generators

Standard generators of A8 are a and b where a is in class 3A, b has order 7, ab has order 6 and abb has order 15.
In the natural representation we may take a = (1, 2, 3) and b = (2, 3, 4, 5, 6, 7, 8).
Standard generators of the double cover 2.A8 are preimages A and B where A has order 3 and B has order 7.

Standard generators of S8 = A8:2 are c and d where c is in class 2C, d has order 7 and cd has order 8.
In the natural representation, we may take c = (1, 2) and d = (2, 3, 4, 5, 6, 7, 8).
Standard generators of either of the double covers 2.S8 are preimages C and D where D has order 7.


The representations of A8 = L4(2) available are: The representations of 2.A8 available are: The representations of S8 = A8:2 available are:
Main ATLAS page Go to main ATLAS (version 2.0) page.
Alternating groups page Go to alternating groups page.
Old A8 page Go to old A8 page - ATLAS version 1.
ftp access Anonymous ftp access is also available on

Version 2.0 created on 14th April 1999.
Last updated 11.03.04 by SJN.
Information checked to Level 1 on 14.04.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.