Is there a way to determine whether a representation of a finite group is faithful?

Question

I want to determine whether a representation of a finite group is faithful from the character table. Is there a such general way or specific way for finite group of small order?

Answer 1

It seems that your question has been settled here:

Faithful representations and character tables

In short, a finite dimensional irreducible representation over $\mathbb{C}$, say $\rho : G \to \operatorname{GL}(V)$, is faithful if and only if $\chi_\rho(g) = \dim V$ only when $g = 1$.