Alternating group A13


Order = 3 113 510 400 = 29.35.52.7.11.13.
Mult = 2.
Out = 2.

Robert Wilson's ATLAS page for A13 is available here.

A13: Length 120, 2-generator, 8-relator.

< x, y | x3 = y11 = (xy)13 = (xy-1xy)2 = (xy-2xy2)2 = (xy-3xy3)2 = (xy-4xy4)2 = (xy-5xy5)2 = 1 >

Remark: Moore/Coxeter presentation (I think). x and y are R.A.Wilson's standard generators for A13. The presentation is available in MAGMA code here. (This applies to the subgroups below too.)

Some subgroups:

Realisation: x = (1, 2, 3) and y = (3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13).
The above permutations are available in MAGMA format here.


S13: Length 123, 2-generator, 8-relator.

< x, y | x13 = y2 = (xy)12 = [x, y]3 = [x2, y]2 = [x3, y]2 = [x4, y]2 = [x5, 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, 9, 10, 11, 12, 13) 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