Symmetric group:S10

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VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This is defined as the symmetric group on a set of size $10$, which for concreteness we can take as the set $\{1,2,3,4,5,6,7,8,9,10\}$. In other words, it is the group of all permutations on nine elements under composition.

In particular, it is a symmetric group on a finite set.

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	3628800	groups with same order	$10!=10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=3628800$