# Symmetric groups are rational-representation

From Groupprops

This article gives the statement, and possibly proof, of a particular group or type of group (namely, Symmetric group (?)) satisfying a particular group property (namely, Rational-representation group (?)).

## Contents

## Statement

Let be a natural number. The symmetric group of degree is a Rational-representation group (?): all its representations over the complex numbers can be realized over the field of rational numbers.

## Related facts

### Weaker facts

### Related facts about alternating groups

- Classification of ambivalent alternating groups
- Finitary alternating group on infinite set is ambivalent