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Let $G$ be a finite group of order $n$. Let $\rho\colon G\rightarrow GL_m(V)$ be a representation with $m>n$ Show that $\rho$ is irreducible.

I have been trying to construct a subrepresentation of order $n$, but have been having no luck.

Any hints would be much appreciated.

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Is this even true? Do you mean "reducible" perhaps? –  Prahlad Vaidyanathan Sep 15 '13 at 19:55
Choose any $0 \ne v \in V$. Then the subspace spanned by $\{\rho(g)(v) : g \in G\}$ is $G$-invariant and has dimension at most $n$. –  Derek Holt Sep 15 '13 at 19:58

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