innerProduct(n,X,Y)
The character table for two characters $X$ and $Y$ of $G$ is calculated using the formula $<X,Y> = \sum_{g \in G} X(g)Y(g) = \sum_{C \in Cl(G)} CX(g_C)Y(g_C) $ where the second sum is taken over all conjugacy classes of $G$ and $g_c$ is an element in the conjugacy class.
As an example we calculate the inner product between the character of the regular representation of $S_4$ and the character indexed by partition {2,1,1}.




As expected this inner product is equal to 3.