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:

M1 = < y, xyx^-1 > = A₁₂ of order 239 500 800 and index 13.

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:

M1 = < xy, y^x > = S₁₂ of order 479 001 600 and index 13.
M2 = < y, xyx^-1yx, x^-2yx² > = S₁₁ x 2 of order 79 833 600 and index 78.

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.

Last updated 27^th June, 1997

John N. Bray

Alternating group A13

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

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

Alternating group A₁₃

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

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