Alternating group A8
Linear group L4(2)

Order = 20 160 = 26.32.5.7.
Mult = 2.
Out = 2.
Robert Wilson's ATLAS page for A8 is available here.

A8: Length 43, 2-generator, 5-relator.

< x, y | x3 = y6 = (xy)7 = [x, y]2 = (xy-2xy2)2 = 1 >

Remark: Moore/Coxeter presentation (I think). The presentation is available in MAGMA code here. (This applies to the subgroups below too.)

Some subgroups:

Realisation: x = (1, 2, 3) and y = (1, 2)(3, 4, 5, 6, 7, 8).
The above permutations are available in MAGMA format here.

S8: Length 64, 2-generator, 6-relator.

< x, y | x8 = y2 = (xy)7 = [x, y]3 = [x2, y]2 = [x3, y]2 = 1 >

Remark: Moore/Coxeter presentation. The presentation is available in MAGMA code here. (This applies to the subgroups below too.)

Some subgroups:

Realisation: x = (1, 2, 3, 4, 5, 6, 7, 8) and y = (1, 2).
The above permutations are available in MAGMA format here.

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- Last updated 27th June, 1997
- John N. Bray