{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Description\n\nThe Tits group ${}^2F_4(2)'$ is the [[commutator subgroup|0ASGSTXSBW]] of the [[Ree group|YB62XEQJAC]] ${}^2F_4(2)$.\nIt has index $2$ in ${}^2F_4(2)$ and its order is\n$$17971200 = 2^{11} \\cdot 3^3 \\cdot 5^2 \\cdot 13.$$\nIt is a finite [[simple group|0YMYMNQ0QZ]], found by Jacques Tits.\n\n## Remarks\n\nThe groups ${}^2F_4(2^{2n+1})$ with $n \\ge 1$ are simple, but ${}^2F_4(2)$ is not, and its simple part is the Tits group.\nSo the Tits group is not strictly a group of Lie type, and it is not counted among the $26$ [[sporadic groups|PZ49Z4CBFZ]] either.\nSome authors list it as a group of Lie type, and others count it as a $27$th sporadic group.\n\n## Explanations\n\n### L1 human\n\nThe Tits group is a single finite simple group that sits at the edge of the classification.\nIt is half of a group of Lie type, so it does not quite fit the families of Lie type and is not usually counted as sporadic.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "object",
    "msc": [
      "20D06",
      "20D08"
    ],
    "name": "Tits group",
    "same_as": {
      "wikidata": "Q2856369",
      "wikipedia": "Tits group"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Tits_group"
      }
    ],
    "tag": "WC16TBY3FN",
    "uses": [
      "YB62XEQJAC",
      "0ASGSTXSBW",
      "0YMYMNQ0QZ",
      "PZ49Z4CBFZ"
    ]
  },
  "kind": "object",
  "link": "https://math2.tamnd.com/node/WC16TBY3FN/",
  "links": [
    {
      "field": "uses",
      "target": "YB62XEQJAC"
    },
    {
      "field": "uses",
      "target": "0ASGSTXSBW"
    },
    {
      "field": "uses",
      "target": "0YMYMNQ0QZ"
    },
    {
      "field": "uses",
      "target": "PZ49Z4CBFZ"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/WC16TBY3FN.md",
  "msc": [
    "20D06",
    "20D08"
  ],
  "name": "Tits group",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/WC1/WC16TBY3FN.md",
  "status": null,
  "tag": "WC16TBY3FN",
  "uri": "m2://WC16TBY3FN",
  "url": "https://math2.tamnd.com/wiki/tits-group/",
  "writing": {
    "tag": "WC16TBY3FN",
    "kind": "object",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}