Finite subgroups of {${\rm GL}\sb {24}({\bf Q})$}

Abstract

We classify maximal finite irreducible subgroups of GL$_{\sans{24}} (\Q)$, together with their natural lattices. There are 65 conjugacy classes of such groups, 41 of which consist of primitive groups. New methods for finding the maximal finite supergroups of irreducible cyclic groups are developed and applied.