Abstract
In this paper, we calculate the numbers of irreducible ordinary characters and irreducible Brauer characters in a block of a finite group G, whose associated fusion system over a 2-subgroup P of G (which is a defect group of the block) has hyperfocal subgroup Z2n×Z2n for a positive integer number n, when the block is controlled by the normalizer NG(P) and the hyperfocal subgroup is contained in the center of P, or when the block is not controlled by NG(P) and the hyperfocal subgroup is contained in the center of the unique essential subgroup in the fusion system and has order at most 16. In particular, Alperin's weight conjecture holds in the considered cases.
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