Alternating group A₇

Order = 2 520 = 2³.3².5.7.
Mult = 6.
Out = 2.

Robert Wilson's ATLAS page for A₇ is available here.

A₇: Length 42, 2-generator, 5-relator.

< x, y | x³ = y⁵ = (xy)⁷ = (xy^-1xy)² = (xy^-2xy²)² = 1 >

Remark: Moore/Coxeter presentation (I think). x and y are R.A.Wilson's standard generators for A₇. The presentation is available in MAGMA code here. (This applies to the subgroups below too.)

Some subgroups:

M1 = < y, xyx^-1 > = A₆ of order 360 and index 7.

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

S₇: Length 45, 2-generator, 5-relator.

< x, y | x⁷ = y² = (xy)⁶ = [x, y]³ = [x², 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 > = S₆ of order 720 and index 7.
M2 = < y, xyx^-1yx, x^-2yx² > = S₅ x 2 of order 240 and index 21.

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

Last updated 25^th August, 1997

John N. Bray

Alternating group A7

A7: Length 42, 2-generator, 5-relator.

S7: Length 45, 2-generator, 5-relator.

Alternating group A₇

A₇: Length 42, 2-generator, 5-relator.

S₇: Length 45, 2-generator, 5-relator.