Comments on the classification of the finite subgroups of SU(3)

Patrick Otto Ludl

Published 2011-01-12, updated 2011-12-19Version 3

Many finite subgroups of SU(3) are commonly used in particle physics. The classification of the finite subgroups of SU(3) began with the work of H.F. Blichfeldt at the beginning of the 20th century. In Blichfeldt's work the two series (C) and (D) of finite subgroups of SU(3) are defined. While the group series Delta(3n^2) and Delta(6n^2) (which are subseries of (C) and (D), respectively) have been intensively studied, there is not much knowledge about the group series (C) and (D). In this work we will show that (C) and (D) have the structures (C) \cong (Z_m x Z_m') \rtimes Z_3 and (D) \cong (Z_n x Z_n') \rtimes S_3, respectively. Furthermore we will show that, while the (C)-groups can be interpreted as irreducible representations of Delta(3n^2), the (D)-groups can in general not be interpreted as irreducible representations of Delta(6n^2).