# Symmetric group:S7

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 group is a finite group defined as the symmetric group on a set of size . The set is typically taken to be .

In particular, it is a symmetric group on finite set as well as a symmetric group of prime degree.

## Arithmetic functions

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

order (number of elements, equivalently, cardinality or size of underlying set) | 5040 | groups with same order | The order is |

exponent of a group | 420 | groups with same order and exponent of a group "{{{" can not be assigned to a declared number type with value 3. | groups with same exponent of a group |
The exponent is the least common multiple of |

Frattini length | 1 | groups with same order and Frattini length "{{{" can not be assigned to a declared number type with value 3. | groups with same Frattini length |