Alternating group A₉

Order = 181 440 = 2⁶.3⁴.5.7.
Mult = 2.
Out = 2.

Robert Wilson's ATLAS page for A₉ is available here.

A₉: Length 64, 2-generator, 6-relator.

< x, y | x³ = y⁷ = (xy)⁹ = (xy^-1xy)² = (xy^-2xy²)² = (xy^-3xy³)² = 1 >

Remark: Moore/Coxeter presentation (I think). x and y are R.A.Wilson's standard generators for A₉. The presentation is available in MAGMA code here. (This applies to the subgroups below too.)

Some subgroups:

M1 = < y, xyx^-1 > = A₈ of order 20 160 and index 9.

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

S₉: Length 67, 2-generator, 6-relator.

< x, y | x⁹ = y² = (xy)⁸ = [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:

M1 = < xy, y^x > = S₈ of order 40 320 and index 9.
M2 = < y, xyx^-1yx, x^-2yx² > = S₇ x 2 of order 10 080 and index 36.

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

Last updated 27^th June, 1997

John N. Bray

Alternating group A9

A9: Length 64, 2-generator, 6-relator.

S9: Length 67, 2-generator, 6-relator.

Alternating group A₉

A₉: Length 64, 2-generator, 6-relator.

S₉: Length 67, 2-generator, 6-relator.