# Symmetric group:S7

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## 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 | 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 |