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Let $G$ be a finite group with faithful irreducible representation $\gamma: G \to GL_n(\mathbb{C})$. , $n>1$.

Can we put a bound on the size of $G$? What if $G$ is nilpotent?

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# Bound on the size of a group given a faithful irrep of a certain dimension

Let $G$ be a finite group with faithful irreducible representation $\gamma: G \to GL_n(\mathbb{C})$.

Can we put a bound on the size of $G$? What if $G$ is nilpotent?