Question 1 Given a representation of a finite group, what algorithm can be used to check is it irreducible or not ?

(Main case - complex numbers, comments on other cases are also welcome. "Given" means finite set of matrices is given).

Question 2 Given a representation of a finite group, what algorithms can be used to decompose it to the direct sum of irreducibles) ?

For the question 1 I would do the following: rep is irrep if its commutant consists of scalar matrices. So I can try to find matrices commuting with all elements of the group and look whether I get only scalar matrices.

Are there more effective ways to do it ?

Related question: How to compute all irreducible representations of a finite group ? (how GAP is doing this?)