On the characterization of the SU(3)-subgroups of type C and D

We investigate the two classes of finite subgroups of SU(3) that are called type C and D in the book of Miller, Blichfeldt and Dickson. We present two theorems which fully determine the form of the generators in a suitable basis. After exploring further properties of these groups, we are able to construct a complete list of infinite series in which these groups are arranged. For type C there are infinitely many series whereas for type D there are only two. Explicit examples of these series are presented which illustrate the general results.