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Symmetric group:S5 - Groupprops

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There are seven conjugacy classes, corresponding to the unordered integer partitions of (for more information, refer cycle type determines conjugacy class). We use the notation of the cycle decomposition for permutations: is a complete group: in particular, every automorphism of the group is inner. Thus, the equivalence classes under automorphisms are the same as the conjugacy classes. In fact, is complete for . See symmetric groups on finite sets are complete. Further information: endomorphism structure of symmetric group:S5 Since is a complete group, it is isomorphic to its automorphism group, where each element of acts on by conjugation. Further information: symmetric groups on finite sets are complete Further information: Subgroup structure of symmetric group:S5 Note that the only normal subgroups are the trivial subgroup, the whole group, and A5 in S5, so we do not waste a column on specifying whether the subgroup is normal and on the quotient group. Further information: lin

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