The authors determine all the absolutely irreducible representations of degree up to 250 of quasi-simple finite groups, excluding groups that are of Lie type in their defining characteristic. Additional information is also given on the Frobenius-Schur indicators and the Brauer character fields of the representations.

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Abstract. The distribution of the unipotent modules (in nondefining prime characteristic) of the finite unitary groups into Harish-Chandra series is investigated. We formulate a series of conjectures relating this distribution with the crystal graph of an integrable module for a certain quantum group. Evidence for our conjectures is presented, as well as proofs for some of their consequences for the crystal graphs involved. In the course of our work we also generalize Harish-Chandra theory for some of the finite classical groups, and we introduce their Harish-Chandra branching graphs.

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