# The number of times each irreducible representation in permutation matrix representation

I am studying a code. One of key part is

Return a list representing the number of times each IRR is present in the permutation matrix representation.

Suppose we have:

1. character table
2. number of inequivalent irreducible representations (just find the length of character table)
3. group order
4. conjugacy classes matrices

The code is the following:

https://sourceforge.net/p/networksym/code/ci/master/tree/networkIRR.py
(def get_IRR_degeneracies(self), particularly)

My question is the following key formula:

total=total +float(len(matricies[j])/group_order)* np.conj(np.complex(characters[i][j]))* np.trace(matricies[j][0])

What is this formula? Where can I find this formula?