How to read labels of character tables in SageMath (and GAP)?

Question

Note: SageMath's Group.character_table() method is built as a wrapper for GAP's CharacterTable() function.

Let $G = \text{Sym}_4$. I would like to be able to extract the character of $G$ indexed by a given partition, say $\lambda = (3,1)$.

I have looked for this online and it seems like this is possible to do in GAP. However, I am struggling to translate GAP commands to SageMath commands in a way that works.

Minimal working example:

sage: G = SymmetricGroup(4)
sage: G.character_table()
[ 1 -1  1  1 -1]
[ 3 -1 -1  0  1]
[ 2  0  2 -1  0]
[ 3  1 -1  0 -1]
[ 1  1  1  1  1]
sage: lam = Partition([3,1])

I want to find a few lines of code that take G and lam and output the character char such that

sage: type(char)
<class 'sage.groups.class_function.ClassFunction_gap'>
sage: char.values()
(3  1 -1  0 -1)

or something similar.

Answer 1

Here it is, just one line:

sage: char = SymmetricGroupRepresentation(lam).to_character()

Indeed:

sage: char.values()
[3, 1, -1, 0, -1]

Alternatively one could implement the Murnaghan–Nakayama rule.