Symmetric groups are rational-representation

Statement
Let $$n$$ be a natural number. The symmetric group of degree $$n$$ is a fact about::rational-representation group: all its representations over the complex numbers can be realized over the field of rational numbers.

Weaker facts

 * Symmetric groups are rational
 * Symmetric groups are ambivalent

Related facts about alternating groups

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

General information pages

 * Linear representation theory of symmetric groups
 * Linear representation theory of alternating groups