The Cayley Table of Symmetric Group ( $S_n$ )

March 25, 2022

Definition. Symmetric Group $S_n$ . See: Subwiki

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S_{3} \text{ has order: }3! = 6

\text{Identity}:\ e=()

$\times$	()	(23)	(12)	(123)	(132)	(13)
()	()	(23)	(12)	(123)	(132)	(13)
(23)	(23)	()	(123)	(12)	(13)	(132)
(12)	(12)	(132)	()	(13)	(23)	(123)
(123)	(123)	(13)	(23)	(132)	()	(12)
(132)	(132)	(12)	(13)	()	(123)	(23)
(13)	(13)	(123)	(132)	(23)	(12)	()

The Cayley Table of Symmetric Group (SnS_nSn​)