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  "body": "\n## Summary\n\nThe nilpotency class of a nilpotent group is the length of its shortest central series.\nIt measures how far the group is from being abelian: the trivial group has class $0$ and a nontrivial abelian group has class $1$.\nIt equals the number of steps that the lower central series, or the upper central series, needs to reach its end.\n\n## Explanations\n\n### L1 human\n\nIn an abelian group, all elements commute.\nIn a nilpotent group, the failure to commute dies out after a fixed number of steps: commutators of commutators of commutators, and so on, become trivial.\nThe class is that number of steps.\nFor example, in the quaternion group $Q_8$ every commutator is $\\pm 1$, and $\\pm 1$ commutes with everything, so $Q_8$ has class $2$.\n",
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