An elementary classification of the quaternionic reflection groups of rank two

Abstract

We give an elementary classification and presentation of the finite quaternionic reflection groups of rank two, based on the notion of a``reflection system''. This simplifies the existing classification, which is shown to be incomplete, e.g., there exist four imprimitive quaternionic reflection groups of order 192 with 22 reflections which are not isomorphic (one of which was previously unknown).