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Note that since the field has characteristic zero, the irreducible representations are the same as indecomposable representations.

Consider the matrix with rows indexed by indecomposable representations, columns indexed by conjugacy classes, and the entry in row <math>\rho</math> and column <math>c</math> is <math>\chi(c,\rho)</math>. ~~In other words, the matrix is the [[character table]]. The automorphism group acts on the rows and on the columns in a way that the entries are not affected. {{further|[[Conjugacy class-representation duality]]}}~~

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