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?
2026-03-26 04:36:42.1774499802
Is there a way to determine whether a representation of a finite group is faithful?
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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 $g = 1$.