Alternating group A12

Order = 239 500 800 = 29.35.52.7.11.
Mult = 2.
Out = 2.
Robert Wilson's ATLAS page for A12 is available here.

A12: Length 91, 2-generator, 7-relator.

< x, y | x3 = y10 = (xy)11 = [x, y]2 = (xy-2xy2)2 = [x, y3]2 = (xy-4xy4)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, 9, 10, 11, 12).
The above permutations are available in MAGMA format here.

S12: Length 120, 2-generator, 8-relator.

< x, y | x12 = y2 = (xy)11 = [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) 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