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The alternating group is defined as the group of all even permutations on a set of 4 elements.
This particular group is solvable
The commutator subgroup of is the Klein group of order 4, namely the normal subgroup comprising double transpositions. This is Abelian.
Thus, is solvable of solvable length 2, or in other words, it is a metabelian group.
This particular group is not nilpotent
This particular group is not Abelian
This particular group is not simple
Since has a proper nontrivial commutator subgroup, it is not simple.