Finite group having the same orbit sizes of conjugacy classes and irreducible representations under automorphism group
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A finite group is said to have the same orbit sizes of conjugacy classes and irreducible representations under automorphism group if the following holds:
Let be the set of conjugacy classes of and be the set of irreducible representations (up to equivalence) of over . The automorphism group acts on both and . The condition we need is that the orbit sizes in and be equal.