Comments on the classification of the finite subgroups of SU(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 Δ(3n2) and Δ(6n2) (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 show that (C) and (D) have the structures and , respectively. Furthermore, we show that, while the (C)-groups can be interpreted as irreducible representations of Δ(3n2), the (D)-groups can in general not be interpreted as irreducible representations of Δ(6n2).

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