The 5-modular characters of the McLaughlin group and its covering group
The authors determine the irreducible Brauer characters and the corresponding decomposition matrices in characteristic 5 for the 3-fold cover \(\hat 3 McL\) of McLaughlin's sporadic simple group \(McL\) of order \(2^ 7\cdot 3^ 6\cdot 5^ 3 \cdot 7\cdot 11\). Apart from 5-blocks of defect 0 the group \(\hat 3 McL\) has three further 5-blocks, the principal block \(B_ 0\) and one ``dual'' pair, say \(B_ 1\), and \(B_ 2=B_ 1^*\) all of which have maximal defect. According to the authors' rule of thumb they use at least one new trick for each block under consideration in order to achieve their goal. On top of that they use the computer system MOC and methods that have become quite standard in that area of research these days, e.g. condensation methods of the Meat-Axe, induction-restriction methods, Nakayama relations, structure of indecomposable modules in a block with cyclic defect group (of order 5 in the present case). It may be worth noting that prior to this work, \textit{A. J. Woldar} [Commun. Algebra 14, 277-291 (1986; Zbl 0581.20007)] determined all but two irreducible Brauer characters of the principal block \(B_ 0\).
scientific article; zbMATH DE number 60117
scientific article