# characterTable -- returns the character table of the symmetric group

## Synopsis

• Usage:
characterTable n
• Inputs:
• n, an integer, the degree of the symmmetric group
• Outputs:
• an instance of the type CharacterTable, the character table with the irreducible characters of $S_n$ indexed by partitions

## Description

This method construct the irreducible characters of $S_n$. The method works by recursively calculating the character tables for the permutation modules of $S_n$. Then applying Gram-Schimdt algorithm to this characters using the inner product of characters we obtain the irreducible characters of $S_n$