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The degree of an irreducible complex character afforded by a finite group is bounded above by the index of an abelian normal subgroup and by the square root of the index of the center. Whenever a finite group affords an irreducible character whose degree achieves these two upper bounds the group must be solvable. Let G be a finite group with an irreducible (complex) character f.doi:10.2307/2036654 fatcat:22vxmi666zfyja4lmfasff5soe