Is there a Sage/Python/ Octave program to compute the irreducible characters of symmetric groups corresponding to different conjugacy classes?
The irreducible characters can be calculated using the determinantal formula or the Murnaghan-Nakayama rule usually. Do we have to write new program to make sage compute this, or, are there built in functions. In case, we need to write a program, which packages should we use? Will the frobenius base change formula be of any use here? Thanks beforehand.
Yes, the method $\text{to_character}$ applied to a given representation of the symmetric group would yield the corresponding characters. The definition of partitions corresponds to conjugacy classes specifies to representations according to which the character is produced, using the $\text{_values}$ function. For more examples and information see here