Alternating group A₁₁

Order = 19 958 400 = 2⁷.3⁴.5².7.11.
Mult = 2.
Out = 2.

Robert Wilson's ATLAS page for A₁₁ is available here.

A₁₁: Length 90, 2-generator, 7-relator.

< x, y | x³ = y⁹ = (xy)¹¹ = (xy^-1xy)² = (xy^-2xy²)² = (xy^-3xy³)² = (xy^-4xy⁴)² = 1 >

Remark: Moore/Coxeter presentation (I think). x and y are R.A.Wilson's standard generators for A₁₁. The presentation is available in MAGMA code here. (This applies to the subgroups below too.)

Some subgroups:

M1 = < y, xyx^-1 > = A₁₀ of order 1 814 400 and index 11.

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

S₁₁: Length 93, 2-generator, 7-relator.

< x, y | x¹¹ = y² = (xy)¹⁰ = [x, y]³ = [x², y]² = [x³, y]² = [x⁴, 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 > = S₁₀ of order 3 628 800 and index 11.
M2 = < y, xyx^-1yx, x^-2yx² > = S₉ x 2 of order 725 760 and index 55.

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

Last updated 27^th June, 1997

John N. Bray

Alternating group A11

A11: Length 90, 2-generator, 7-relator.

S11: Length 93, 2-generator, 7-relator.

Alternating group A₁₁

A₁₁: Length 90, 2-generator, 7-relator.

S₁₁: Length 93, 2-generator, 7-relator.