If \(G\) is a finite subgroup of \(GL(3,{\mathbb C})\), then \(G\) acts on \({\mathbb C}^3\), and it is known that \({\mathbb C}^3/G\) is Gorenstein if and only if \(G\) is a subgroup of \(SL(3,{\mathbb C})\). In this work, the authors begin with a classification of finite subgroups of \(SL(3,{\mathbb C})\), including two types, (J) and (K), which have often been overlooked. They go on to present a general method for finding invariant polynomials and their relations to finite subgroups of \(GL(3,{\mathbb C})\). The method is, in practice, substantially better than the classical method due to Noether. Some properties of quotient varieties are presented, along with a proof that \({\mathbb C}^3/G\) has isolated singularities if and only if \(G\) is abelian and 1 is not an eigenvalue of \(g\) for every nontrivial \(g \in G\). The authors also find minimal quotient generators of the ring of invariant polynomials and relations among them.