Multiply transitive permutation group
Classification

Permutation group

Multiply transitive permutation group

A permutation group $𝐺 \subseteq Ω!$ is $𝑘$ -transitive iff it acts on ordered tuples in $Ω P 𝑘$ transitively. group

Classification

For $𝑘 \geq 6$ , the only $𝑘$ -transitive groups are $S 𝑛$ with $𝑛 \geq 𝑘$ and $A l t 𝑛$ with $𝑛 \geq 𝑘 + 2$ ;
The only 5-transitive groups that aren’t 6-transitive are Mathieu group M24, Mathieu group M12, [[Symmetric group| $S 5$ ]], and [[Alternating group| $A l t 7$ ]].

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Alternating group
Mathieu group M24
Permutation group

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