Symchar is a python package for generating character tables of symmetric groups.

>>> import symchar
>>> c = symchar.character_table(3)
>>> c
CharacterTable([[ 1,  1,  1],
            [-1,  0,  2],
            [ 1, -1,  1]], dtype=object)

There is some support for basic operations on characters, such as decomposing the tensor product.

>>> c.tensor_product_decomposition(c[1], c[1])
{[3]: 1, [2, 1]: 1, [1, 1, 1]: 1}

The rows and columns of the character table of S_n are indexed by the partitions of n with respect to the dominance order, but you can also look up characters by passing a Partition object.

from symchar import Partition
>>> mu = Partition([2, 1])
>>> c.get_character(mu)
CharacterTable([-1, 0, 2], dtype=object)

The method for constructing the character table follows Lecture 6 of G.D. James' The Representation Theory of Symmetric Groups.

This was a toy project to generate data for a toy project on predicting kronecker coefficients. This only required character tables up to n=15, which takes a few seconds with symchar. If you want to work with larger symmetric groups, you should probably use something like GAP.