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We study the representation growth of alternating and symmetric groups inpositive characteristic and restricted representation growth for the finitegroups of Lie type. We show that the the number of representations of dimensionat most n is bounded by a low degree polynomial in n. As a consequence, we showthat the number of conjugacy classes of maximal subgroups of a finite almostsimple group G is at most O(log|G|).

Representation Growth in positive characteristic and conjugacy classes of maximal subgroups