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  "body": "\n## Definition\n\nLet $G$ be a [[group|G5S1M9]] with a [[composition series|0XV2A49X6Q]] $\\{e\\} = G_0 \\trianglelefteq G_1 \\trianglelefteq \\cdots \\trianglelefteq G_n = G$.\nThe composition factors of $G$ are the simple groups $G_i / G_{i-1}$ for $i = 1, \\dots, n$, counted with multiplicity.\nThe number $n$ is the composition length of $G$.\n\n## Remarks\n\nThe [[Jordan–Hölder theorem|0E088ZP533]] shows that the composition factors do not depend on the series, up to order and isomorphism.\nThe composition factors of $\\mathbb{Z}/12\\mathbb{Z}$ are $\\mathbb{Z}/2\\mathbb{Z}$, $\\mathbb{Z}/2\\mathbb{Z}$ and $\\mathbb{Z}/3\\mathbb{Z}$.\nThe composition factors of $S_4$ are $\\mathbb{Z}/2\\mathbb{Z}$, $\\mathbb{Z}/3\\mathbb{Z}$, $\\mathbb{Z}/2\\mathbb{Z}$ and $\\mathbb{Z}/2\\mathbb{Z}$.\nGroups that are not isomorphic can have the same composition factors, for example $\\mathbb{Z}/4\\mathbb{Z}$ and $\\mathbb{Z}/2\\mathbb{Z} \\times \\mathbb{Z}/2\\mathbb{Z}$.\n\n## Explanations\n\n### L1 human\n\nThe composition factors are the simple pieces of a group.\nThey are like the prime factors of an integer, counted with multiplicity.\nBut unlike for integers, the pieces do not determine the group.\n",
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