"S4 Multiplication Chart"

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S
Multiplication Table
4
a
ga
A
A
coset
4
4
g
1
(1 2)(3 4) (1 3)(2 4) (1 4)(2 3) (1 2 3)
(1 2 4)
(1 3 2)
(1 3 4)
(1 4 2)
(1 4 3)
(2 3 4)
(2 4 3)
(1 2)
(1 3)
(1 4)
(2 3)
(2 4)
(3 4)
(1 2 3 4) (1 2 4 3) (1 3 2 4) (1 3 4 2) (1 4 2 3) (1 4 3 2)
1
1
(1 2)(3 4) (1 3)(2 4) (1 4)(2 3) (1 2 3)
(1 2 4)
(1 3 2)
(1 3 4)
(1 4 2)
(1 4 3)
(2 3 4)
(2 4 3)
(1 2)
(1 3)
(1 4)
(2 3)
(2 4)
(3 4)
(1 2 3 4) (1 2 4 3) (1 3 2 4) (1 3 4 2) (1 4 2 3) (1 4 3 2)
(1 2)(3 4) (1 2)(3 4)
1
(1 4)(2 3) (1 3)(2 4) (2 4 3)
(2 3 4)
(1 4 3)
(1 4 2)
(1 3 4)
(1 3 2)
(1 2 4)
(1 2 3)
(3 4)
(1 4 3 2) (1 3 4 2) (1 2 4 3) (1 2 3 4)
(1 2)
(2 4)
(2 3)
(1 4 2 3)
(1 4)
(1 3 2 4)
(1 3)
(1 3)(2 4) (1 3)(2 4) (1 4)(2 3)
1
(1 2)(3 4) (1 4 2)
(1 4 3)
(2 3 4)
(2 4 3)
(1 2 3)
(1 2 4)
(1 3 2)
(1 3 4)
(1 4 2 3)
(2 4)
(1 2 4 3) (1 3 4 2)
(1 3)
(1 3 2 4) (1 4 3 2)
(1 4)
(3 4)
(2 3)
(1 2)
(1 2 3 4)
(1 4)(2 3) (1 4)(2 3) (1 3)(2 4) (1 2)(3 4)
1
( 1 3 4)
(1 3 2)
(1 2 4)
(1 2 3)
(2 4 3)
(2 3 4)
(1 4 3)
(1 4 2)
(1 3 2 4) (1 2 3 4)
(2 3)
(1 4)
(1 4 3 2) (1 4 2 3)
(1 3)
(1 3 4 2)
(1 2)
(1 2 4 3)
(3 4)
(2 4)
(1 2 3)
(1 2 3)
(1 3 4)
(2 4 3)
(1 4 2)
(1 3 2) (1 3)(2 4)
1
(2 3 4)
(1 4 3) (1 4)(2 3) (1 2)(3 4) (1 2 4)
(1 3)
(2 3)
(1 4 2 3)
(1 2)
(1 2 4 3) (1 2 3 4) (1 3 4 2) (1 3 2 4)
(2 4)
(3 4)
(1 4 3 2)
(1 4)
(1 2 4)
(1 2 4)
(1 4 3)
(1 3 2)
(2 3 4) (1 4)(2 3) (1 4 2)
(1 3 4) (1 3)(2 4)
1
(2 4 3)
(1 2 3) (1 2)(3 4)
(1 4)
(1 3 2 4)
(2 4)
(1 2 3 4)
(1 2)
(1 2 4 3) (1 4 2 3) (1 4 3 2) (1 3 4 2)
(1 3)
(2 3)
(3 4)
(1 3 2)
(1 3 2)
(2 3 4)
(1 2 4)
(1 4 3)
1
(2 4 3)
(1 2 3) (1 2)(3 4) (1 4)(2 3) (1 4 2)
(1 3 4) (1 3)(2 4)
(2 3)
(1 2)
(1 4 3 2)
(1 3)
(1 3 2 4) (1 3 4 2)
(3 4)
(2 4)
(1 2 4 3) (1 2 3 4)
(1 4)
(1 4 2 3)
(1 3 4)
(1 3 4)
(1 2 3)
(1 4 2)
(2 4 3)
(1 2 4) (1 2)(3 4) (1 4)(2 3) (1 4 3)
(2 3 4)
1
(1 3)(2 4) (1 3 2)
(1 2 3 4)
(1 4)
(3 4)
(1 3 2 4) (1 3 4 2)
(1 3)
(1 2 4 3)
(1 2)
(1 4 3 2) (1 4 2 3)
(2 4)
(2 3)
(1 4 2)
(1 4 2)
(2 4 3)
(1 3 4)
(1 2 3)
(2 3 4)
1
(1 3)(2 4) (1 3 2)
(1 2 4) (1 2)(3 4) (1 4)(2 3) (1 4 3)
(2 4)
(1 3 4 2)
(1 2)
(1 4 2 3)
(1 4)
(1 4 3 2)
(2 3)
(3 4)
(1 3)
(1 3 2 4) (1 2 3 4) (1 2 4 3)
(1 4 3)
(1 4 3)
(1 2 4)
(2 3 4)
(1 3 2) (1 2)(3 4) (1 2 3)
(2 4 3)
1
(1 3)(2 4) (1 3 4)
(1 4 2) (1 4)(2 3) (1 2 4 3)
(3 4)
(1 3)
(1 4 3 2) (1 4 2 3)
(1 4)
(1 2)
(1 2 3 4)
(2 3)
(2 4)
(1 3 4 2) (1 3 2 4)
(2 3 4)
(2 3 4)
(1 3 2)
(1 4 3)
(1 2 4) (1 3)(2 4) (1 3 4)
(1 4 2) (1 4)(2 3) (1 2)(3 4) (1 2 3)
(2 4 3)
1
(1 3 4 2) (1 4 2 3) (1 2 3 4)
(2 4)
(3 4)
(2 3)
(1 3 2 4)
(1 3)
(1 4)
(1 4 3 2) (1 2 4 3)
(1 2)
(2 4 3)
(2 4 3)
(1 4 2)
(1 2 3)
(1 3 4)
(1 4 3) (1 4)(2 3) (1 2)(3 4) (1 2 4)
(1 3 2) (1 3)(2 4)
1
(2 3 4)
(1 4 3 2) (1 2 4 3) (1 3 2 4)
(3 4)
(2 3)
(2 4)
(1 4)
(1 4 2 3) (1 2 3 4)
(1 2)
(1 3)
(1 3 4 2)
(1 2)
(1 2)
(3 4)
(1 3 2 4) (1 4 2 3)
(2 3)
(2 4)
(1 3)
(1 3 4 2)
(1 4)
(1 4 3 2) (1 2 3 4) (1 2 4 3)
1
(1 3 2)
(1 4 2)
(1 2 3)
(1 2 4) (1 2)(3 4) (2 3 4)
(2 4 3) (1 3)(2 4) (1 3 4) (1 4)(2 3) (1 4 3)
(1 3)
(1 3)
(1 2 3 4)
(2 4)
(1 4 3 2)
(1 2)
(1 2 4 3)
(2 3)
(3 4)
(1 4 2 3)
(1 4)
(1 3 4 2) (1 3 2 4)
(1 2 3)
1
(1 4 3)
(1 3 2) (1 3)(2 4) (1 3 4) (1 2)(3 4) (1 2 4)
(2 4 3)
(2 3 4)
(1 4 2) (1 4)(2 3)
(1 4)
(1 4)
(1 2 4 3) (1 3 4 2)
(2 3)
(1 2 3 4)
(1 2)
(1 3 2 4)
(1 3)
(2 4)
(3 4)
(1 4 2 3) (1 4 3 2)
(1 2 4)
(1 3 4)
1
(1 4)(2 3) (1 4 2)
(1 4 3)
(1 2 3) (1 2)(3 4) (1 3 2) (1 3)(2 4) (2 3 4)
(2 4 3)
(2 3)
(2 3)
(1 3 4 2) (1 2 4 3)
(1 4)
(1 3)
(1 3 2 4)
(1 2)
(1 2 3 4) (1 4 3 2) (1 4 2 3)
(3 4)
(2 4)
(1 3 2)
(1 2 3) (1 4)(2 3)
1
(2 4 3)
(2 3 4)
(1 3 4) (1 3)(2 4) (1 2 4) (1 2)(3 4) (1 4 3)
(1 4 2)
(2 4)
(2 4)
(1 4 3 2)
(1 3)
(1 2 3 4) (1 4 2 3)
(1 4)
(1 3 4 2) (1 3 2 4)
(1 2)
(1 2 4 3)
(2 3)
(3 4)
(1 4 2) (1 3)(2 4) (1 2 4)
(2 3 4)
1
(2 4 3) (1 4)(2 3) (1 4 3)
(1 3 4)
(1 3 2)
(1 2 3) (1 2)(3 4)
(3 4)
(3 4)
(1 2)
(1 4 2 3) (1 3 2 4) (1 2 4 3) (1 2 3 4) (1 4 3 2)
(1 4)
(1 3 4 2)
(1 3)
(2 4)
(2 3)
(1 2)(3 4) (1 4 3)
(1 3 4)
(2 4 3)
(2 3 4)
1
(1 2 4)
(1 2 3) (1 4)(2 3) (1 4 2) (1 3)(2 4) (1 3 2)
(1 2 3 4)
(1 2 3 4)
(1 3)
(1 4 3 2)
(2 4)
(1 3 2 4) (1 3 4 2)
(1 4)
(1 4 2 3)
(3 4)
(2 3)
(1 2 4 3)
(1 2)
(1 3 4) (1 4)(2 3) (2 3 4)
(1 2 4) (1 2)(3 4) (1 2 3) (1 3)(2 4) (1 3 2)
(1 4 2)
(1 4 3)
(2 4 3)
1
(1 2 4 3)
(1 2 4 3)
(1 4)
(2 3)
(1 3 4 2) (1 4 3 2) (1 4 2 3)
(3 4)
(2 4)
(1 3)
(1 3 2 4)
(1 2)
(1 2 3 4)
(1 4 3)
(2 4 3) (1 3)(2 4) (1 2)(3 4) (1 2 3)
(1 2 4)
(1 4 2) (1 4)(2 3) (2 3 4)
1
(1 3 2)
(1 3 4)
(1 3 2 4)
(1 3 2 4) (1 4 2 3)
(1 2)
(3 4)
(1 4)
(1 4 3 2) (1 2 3 4) (1 2 4 3)
(2 3)
(2 4)
(1 3)
(1 3 4 2) (1 4)(2 3) (1 2 4)
(2 4 3)
(1 3 4)
(1 3 2) (1 3)(2 4) (1 4 3)
(1 4 2) (1 2)(3 4) (1 2 3)
1
(2 3 4)
(1 3 4 2)
(1 3 4 2)
(2 3)
(1 4)
(1 2 4 3)
(2 4)
(3 4)
(1 4 2 3) (1 4 3 2) (1 2 3 4)
(1 2)
(1 3 2 4)
(1 3)
(2 3 4)
(1 4 2) (1 2)(3 4) (1 3)(2 4) (1 3 4)
(1 3 2)
(2 4 3)
1
(1 4 3) (1 4)(2 3) (1 2 4)
(1 2 3)
(1 4 2 3)
(1 4 2 3) (1 3 2 4)
(3 4)
(1 2)
(1 3 4 2)
(1 3)
(2 4)
(2 3)
(1 2 4 3) (1 2 3 4) (1 4 3 2)
(1 4)
(1 3)(2 4) (2 3 4)
(1 2 3)
(1 4 2)
(1 4 3) (1 4)(2 3) (1 3 2)
(1 3 4)
1
(2 4 3) (1 2)(3 4) (1 2 4)
(1 4 3 2)
(1 4 3 2)
(2 4)
(1 2 3 4)
(1 3)
(3 4)
(2 3)
(1 2 4 3)
(1 2)
(1 3 2 4) (1 3 4 2)
(1 4)
(1 4 2 3)
(2 4 3) (1 2)(3 4) (1 3 2)
(1 4 3) (1 4)(2 3) (1 4 2)
1
(2 3 4)
(1 2 3)
(1 2 4)
(1 3 4) (1 3)(2 4)
S
Multiplication Table
4
a
ga
A
A
coset
4
4
g
1
(1 2)(3 4) (1 3)(2 4) (1 4)(2 3) (1 2 3)
(1 2 4)
(1 3 2)
(1 3 4)
(1 4 2)
(1 4 3)
(2 3 4)
(2 4 3)
(1 2)
(1 3)
(1 4)
(2 3)
(2 4)
(3 4)
(1 2 3 4) (1 2 4 3) (1 3 2 4) (1 3 4 2) (1 4 2 3) (1 4 3 2)
1
1
(1 2)(3 4) (1 3)(2 4) (1 4)(2 3) (1 2 3)
(1 2 4)
(1 3 2)
(1 3 4)
(1 4 2)
(1 4 3)
(2 3 4)
(2 4 3)
(1 2)
(1 3)
(1 4)
(2 3)
(2 4)
(3 4)
(1 2 3 4) (1 2 4 3) (1 3 2 4) (1 3 4 2) (1 4 2 3) (1 4 3 2)
(1 2)(3 4) (1 2)(3 4)
1
(1 4)(2 3) (1 3)(2 4) (2 4 3)
(2 3 4)
(1 4 3)
(1 4 2)
(1 3 4)
(1 3 2)
(1 2 4)
(1 2 3)
(3 4)
(1 4 3 2) (1 3 4 2) (1 2 4 3) (1 2 3 4)
(1 2)
(2 4)
(2 3)
(1 4 2 3)
(1 4)
(1 3 2 4)
(1 3)
(1 3)(2 4) (1 3)(2 4) (1 4)(2 3)
1
(1 2)(3 4) (1 4 2)
(1 4 3)
(2 3 4)
(2 4 3)
(1 2 3)
(1 2 4)
(1 3 2)
(1 3 4)
(1 4 2 3)
(2 4)
(1 2 4 3) (1 3 4 2)
(1 3)
(1 3 2 4) (1 4 3 2)
(1 4)
(3 4)
(2 3)
(1 2)
(1 2 3 4)
(1 4)(2 3) (1 4)(2 3) (1 3)(2 4) (1 2)(3 4)
1
( 1 3 4)
(1 3 2)
(1 2 4)
(1 2 3)
(2 4 3)
(2 3 4)
(1 4 3)
(1 4 2)
(1 3 2 4) (1 2 3 4)
(2 3)
(1 4)
(1 4 3 2) (1 4 2 3)
(1 3)
(1 3 4 2)
(1 2)
(1 2 4 3)
(3 4)
(2 4)
(1 2 3)
(1 2 3)
(1 3 4)
(2 4 3)
(1 4 2)
(1 3 2) (1 3)(2 4)
1
(2 3 4)
(1 4 3) (1 4)(2 3) (1 2)(3 4) (1 2 4)
(1 3)
(2 3)
(1 4 2 3)
(1 2)
(1 2 4 3) (1 2 3 4) (1 3 4 2) (1 3 2 4)
(2 4)
(3 4)
(1 4 3 2)
(1 4)
(1 2 4)
(1 2 4)
(1 4 3)
(1 3 2)
(2 3 4) (1 4)(2 3) (1 4 2)
(1 3 4) (1 3)(2 4)
1
(2 4 3)
(1 2 3) (1 2)(3 4)
(1 4)
(1 3 2 4)
(2 4)
(1 2 3 4)
(1 2)
(1 2 4 3) (1 4 2 3) (1 4 3 2) (1 3 4 2)
(1 3)
(2 3)
(3 4)
(1 3 2)
(1 3 2)
(2 3 4)
(1 2 4)
(1 4 3)
1
(2 4 3)
(1 2 3) (1 2)(3 4) (1 4)(2 3) (1 4 2)
(1 3 4) (1 3)(2 4)
(2 3)
(1 2)
(1 4 3 2)
(1 3)
(1 3 2 4) (1 3 4 2)
(3 4)
(2 4)
(1 2 4 3) (1 2 3 4)
(1 4)
(1 4 2 3)
(1 3 4)
(1 3 4)
(1 2 3)
(1 4 2)
(2 4 3)
(1 2 4) (1 2)(3 4) (1 4)(2 3) (1 4 3)
(2 3 4)
1
(1 3)(2 4) (1 3 2)
(1 2 3 4)
(1 4)
(3 4)
(1 3 2 4) (1 3 4 2)
(1 3)
(1 2 4 3)
(1 2)
(1 4 3 2) (1 4 2 3)
(2 4)
(2 3)
(1 4 2)
(1 4 2)
(2 4 3)
(1 3 4)
(1 2 3)
(2 3 4)
1
(1 3)(2 4) (1 3 2)
(1 2 4) (1 2)(3 4) (1 4)(2 3) (1 4 3)
(2 4)
(1 3 4 2)
(1 2)
(1 4 2 3)
(1 4)
(1 4 3 2)
(2 3)
(3 4)
(1 3)
(1 3 2 4) (1 2 3 4) (1 2 4 3)
(1 4 3)
(1 4 3)
(1 2 4)
(2 3 4)
(1 3 2) (1 2)(3 4) (1 2 3)
(2 4 3)
1
(1 3)(2 4) (1 3 4)
(1 4 2) (1 4)(2 3) (1 2 4 3)
(3 4)
(1 3)
(1 4 3 2) (1 4 2 3)
(1 4)
(1 2)
(1 2 3 4)
(2 3)
(2 4)
(1 3 4 2) (1 3 2 4)
(2 3 4)
(2 3 4)
(1 3 2)
(1 4 3)
(1 2 4) (1 3)(2 4) (1 3 4)
(1 4 2) (1 4)(2 3) (1 2)(3 4) (1 2 3)
(2 4 3)
1
(1 3 4 2) (1 4 2 3) (1 2 3 4)
(2 4)
(3 4)
(2 3)
(1 3 2 4)
(1 3)
(1 4)
(1 4 3 2) (1 2 4 3)
(1 2)
(2 4 3)
(2 4 3)
(1 4 2)
(1 2 3)
(1 3 4)
(1 4 3) (1 4)(2 3) (1 2)(3 4) (1 2 4)
(1 3 2) (1 3)(2 4)
1
(2 3 4)
(1 4 3 2) (1 2 4 3) (1 3 2 4)
(3 4)
(2 3)
(2 4)
(1 4)
(1 4 2 3) (1 2 3 4)
(1 2)
(1 3)
(1 3 4 2)
(1 2)
(1 2)
(3 4)
(1 3 2 4) (1 4 2 3)
(2 3)
(2 4)
(1 3)
(1 3 4 2)
(1 4)
(1 4 3 2) (1 2 3 4) (1 2 4 3)
1
(1 3 2)
(1 4 2)
(1 2 3)
(1 2 4) (1 2)(3 4) (2 3 4)
(2 4 3) (1 3)(2 4) (1 3 4) (1 4)(2 3) (1 4 3)
(1 3)
(1 3)
(1 2 3 4)
(2 4)
(1 4 3 2)
(1 2)
(1 2 4 3)
(2 3)
(3 4)
(1 4 2 3)
(1 4)
(1 3 4 2) (1 3 2 4)
(1 2 3)
1
(1 4 3)
(1 3 2) (1 3)(2 4) (1 3 4) (1 2)(3 4) (1 2 4)
(2 4 3)
(2 3 4)
(1 4 2) (1 4)(2 3)
(1 4)
(1 4)
(1 2 4 3) (1 3 4 2)
(2 3)
(1 2 3 4)
(1 2)
(1 3 2 4)
(1 3)
(2 4)
(3 4)
(1 4 2 3) (1 4 3 2)
(1 2 4)
(1 3 4)
1
(1 4)(2 3) (1 4 2)
(1 4 3)
(1 2 3) (1 2)(3 4) (1 3 2) (1 3)(2 4) (2 3 4)
(2 4 3)
(2 3)
(2 3)
(1 3 4 2) (1 2 4 3)
(1 4)
(1 3)
(1 3 2 4)
(1 2)
(1 2 3 4) (1 4 3 2) (1 4 2 3)
(3 4)
(2 4)
(1 3 2)
(1 2 3) (1 4)(2 3)
1
(2 4 3)
(2 3 4)
(1 3 4) (1 3)(2 4) (1 2 4) (1 2)(3 4) (1 4 3)
(1 4 2)
(2 4)
(2 4)
(1 4 3 2)
(1 3)
(1 2 3 4) (1 4 2 3)
(1 4)
(1 3 4 2) (1 3 2 4)
(1 2)
(1 2 4 3)
(2 3)
(3 4)
(1 4 2) (1 3)(2 4) (1 2 4)
(2 3 4)
1
(2 4 3) (1 4)(2 3) (1 4 3)
(1 3 4)
(1 3 2)
(1 2 3) (1 2)(3 4)
(3 4)
(3 4)
(1 2)
(1 4 2 3) (1 3 2 4) (1 2 4 3) (1 2 3 4) (1 4 3 2)
(1 4)
(1 3 4 2)
(1 3)
(2 4)
(2 3)
(1 2)(3 4) (1 4 3)
(1 3 4)
(2 4 3)
(2 3 4)
1
(1 2 4)
(1 2 3) (1 4)(2 3) (1 4 2) (1 3)(2 4) (1 3 2)
(1 2 3 4)
(1 2 3 4)
(1 3)
(1 4 3 2)
(2 4)
(1 3 2 4) (1 3 4 2)
(1 4)
(1 4 2 3)
(3 4)
(2 3)
(1 2 4 3)
(1 2)
(1 3 4) (1 4)(2 3) (2 3 4)
(1 2 4) (1 2)(3 4) (1 2 3) (1 3)(2 4) (1 3 2)
(1 4 2)
(1 4 3)
(2 4 3)
1
(1 2 4 3)
(1 2 4 3)
(1 4)
(2 3)
(1 3 4 2) (1 4 3 2) (1 4 2 3)
(3 4)
(2 4)
(1 3)
(1 3 2 4)
(1 2)
(1 2 3 4)
(1 4 3)
(2 4 3) (1 3)(2 4) (1 2)(3 4) (1 2 3)
(1 2 4)
(1 4 2) (1 4)(2 3) (2 3 4)
1
(1 3 2)
(1 3 4)
(1 3 2 4)
(1 3 2 4) (1 4 2 3)
(1 2)
(3 4)
(1 4)
(1 4 3 2) (1 2 3 4) (1 2 4 3)
(2 3)
(2 4)
(1 3)
(1 3 4 2) (1 4)(2 3) (1 2 4)
(2 4 3)
(1 3 4)
(1 3 2) (1 3)(2 4) (1 4 3)
(1 4 2) (1 2)(3 4) (1 2 3)
1
(2 3 4)
(1 3 4 2)
(1 3 4 2)
(2 3)
(1 4)
(1 2 4 3)
(2 4)
(3 4)
(1 4 2 3) (1 4 3 2) (1 2 3 4)
(1 2)
(1 3 2 4)
(1 3)
(2 3 4)
(1 4 2) (1 2)(3 4) (1 3)(2 4) (1 3 4)
(1 3 2)
(2 4 3)
1
(1 4 3) (1 4)(2 3) (1 2 4)
(1 2 3)
(1 4 2 3)
(1 4 2 3) (1 3 2 4)
(3 4)
(1 2)
(1 3 4 2)
(1 3)
(2 4)
(2 3)
(1 2 4 3) (1 2 3 4) (1 4 3 2)
(1 4)
(1 3)(2 4) (2 3 4)
(1 2 3)
(1 4 2)
(1 4 3) (1 4)(2 3) (1 3 2)
(1 3 4)
1
(2 4 3) (1 2)(3 4) (1 2 4)
(1 4 3 2)
(1 4 3 2)
(2 4)
(1 2 3 4)
(1 3)
(3 4)
(2 3)
(1 2 4 3)
(1 2)
(1 3 2 4) (1 3 4 2)
(1 4)
(1 4 2 3)
(2 4 3) (1 2)(3 4) (1 3 2)
(1 4 3) (1 4)(2 3) (1 4 2)
1
(2 3 4)
(1 2 3)
(1 2 4)
(1 3 4) (1 3)(2 4)