Least $n$ such that it is possible to embed

Groups, Rings, Domains, Modules, etc, Galois theory
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Tolaso J Kos
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Least $n$ such that it is possible to embed

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Post by Tolaso J Kos »

Let $\operatorname{GL}_2(\mathbb{F}_5)$ be the group of invertible $2\times 2$ matrices over $\mathbb{F}_5$, and $\mathcal{S}_n$ be the group of permutations of $n$ objects. What is the least $n\in\mathbb{N}$ such that there is an embedding (injective homomorphism) of $\operatorname{GL}_2(\mathbb{F}_5)$ into $\mathcal{S}_n$?
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Imagination is much more important than knowledge.
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