On the finite subgroups of U(3) of order smaller than 512

Understand

We use the SmallGroups Library to find the finite subgroups of U(3) of order smaller than 512 which possess a faithful three-dimensional irreducible representation.

• From the resulting list of groups we extract those groups that can not be written as direct products with cyclic groups.
• These groups are the basic building blocks for models based on finite subgroups of U(3).
• All resulting finite subgroups of SU(3) can be identified using the well known list of finite subgroups of SU(3) derived by Miller, Blichfeldt and Dickson at the beginning of the 20th century.