A **permutation representation** of a finite group $G$ is a homomorphism $\rho : G \to S_n$ for some $n$. The integer $n$ is the **degree** of $\rho$, and a representation is **faithful** if $\rho$ is injective. The representation is **transitive** if the set $\{1, \dots, n\}$ cannot be broken up into smaller orbits under the action of $G$, i.e. for all $1 \le i \le j \le n$ there is some $g \in G$ with $\rho(g)(i) = j$.

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- Last edited by Jennifer Paulhus on 2022-07-19 08:53:14

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