In general, a representation of a finite group with a finite carrier space is a homomorphism ,
i.e. representation matrices of finite group elements have determinant 1. #m/thm/rep
Proof
Let be a finite group and be a representation thereof with finite carrier space.
Assume there exists such that .
Then for all , and therefore for all .
Thus the cyclic subgroup is infinite, contradicting our requirement.
Therefore for all