TITLE: Is there a systematic way to determine the irreducible representations of a finite group?
QUESTION [6 upvotes]: I was reading through fulton and harris's book on representation theory. I'm in the middle of chapter 3 and noticed their approach to finding irreducible representations of groups is pretty exploratory. I see no reason to believe the methods employed should always work. 
So, I was wondering is there an efficient method to find all the irreducible representations of a given finite group?

REPLY [3 votes]: The answer is that efficient algorithms to find the irreducible representations of a finite group do exist, but they are beyond the scope of a first course in representation theory.  See the following question on Math Overflow:
How to compute all irreducible representations of a finite group ? (how GAP is doing this?)