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# Dom::SymmetricGroup

Symmetric groups

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```Dom::SymmetricGroup(n)
Dom::SymmetricGroup(n)(l)
```

## Description

Dom::SymmetricGroup(n) creates the symmetric group of order n, that is, the domain of all the permutations of {1, …, n} elements.

A permutation of n elements is a bijective mapping of the set {1, …, n} onto itself.

The domain element Dom::SymmetricGroup(n)(l) represents the bijective mapping of the first n positive integers that maps the integer i to l[i], for 1 ≤ in.

Dom::BaseDomain

Ax::canonicalRep

Cat::Group

## Examples

### Example 1

Consider the group of permutations of the first seven positive integers:

`G := Dom::SymmetricGroup(7)`

We create an element of G by providing the image of 1, 2, etc.:

`a:=G([2,4,6,1,3,5,7])`

`a(3)`

## Parameters

 n Positive integer l List or array consisting of the first n integers in some order.

## Entries

 "one" the identical mapping of the set {1, …, n} to itself.

expand all

## Mathematical Methods

### _mult — Product of permutations

_mult(a1, …)

This method overloads the function _mult.

### _invert — Inverse of a permutation

_invert(a)

This method overloads the function _invert.

### func_call — Function value of a permutation at a point

func_call(a, i)

It computes the function value of a at i, i.e., the integer that i is mapped to by the permutation a; i must be an integer between 1 and n.

cycles(a)

order(a)

inversions(a)

sign(a)

random()

allElements()

size()

convert(x)

convert_to(a, T)

expr(a)