Symmetric group:S10

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This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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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