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Let G$G$ be a finite simple group, and let n$n$ be the smallest integer such that there exists an embedding of G$G$ into the permutation group of n$n$ elements. Is this embedding unique up to conjugation?

Let G be a finite simple group, and let n be the smallest integer such that there exists an embedding of G into the permutation group of n elements. Is this embedding unique up to conjugation?

Let $G$ be a finite simple group, and let $n$ be the smallest integer such that there exists an embedding of $G$ into the permutation group of $n$ elements. Is this embedding unique up to conjugation?

added condition mentioned in the comments
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Arturo Magidin
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Let G be a finite simple group, and let n be the smallest integer such that there exists an embedding of G into the permutation group of n elements. Is this embedding unique up to conjugation?

Let G be a finite group, and let n be the smallest integer such that there exists an embedding of G into the permutation group of n elements. Is this embedding unique up to conjugation?

Let G be a finite simple group, and let n be the smallest integer such that there exists an embedding of G into the permutation group of n elements. Is this embedding unique up to conjugation?

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Shaki
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embeddings of finite group into permutation groups

Let G be a finite group, and let n be the smallest integer such that there exists an embedding of G into the permutation group of n elements. Is this embedding unique up to conjugation?