Let us assume I have a matrix representation for an algebraic group.
Do there exist linear algebraic algorithms to simultaneous block factorization like this:
$$\bf M_i = SC_iS^{-1}$$
Where $\bf M_i$ is representation matrix for element $i$ and so the $\bf C_i$ correspond to group operation on element $i$ in irreducible representation (maximally "squeezed" diagonal block-matrices)?