# Symmetric group:S9

From Groupprops

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 groupView a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## Definition

This is defined as the symmetric group on a set of size , which for concreteness we can take as the set . 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 and also a symmetric group of prime power degree.

## Arithmetic functions

Function | Value | Similar groups | Explanation |
---|---|---|---|

order (number of elements, equivalently, cardinality or size of underlying set) | 362880 | groups with same order |