---
tag: WC16TBY3FN
kind: object
name: Tits group
msc: [20D06, 20D08]
uses: [YB62XEQJAC, 0ASGSTXSBW, 0YMYMNQ0QZ, PZ49Z4CBFZ]
sources:
  - url: https://en.wikipedia.org/wiki/Tits_group
same_as:
  wikidata: Q2856369
  wikipedia: Tits group
---

## Description

The Tits group ${}^2F_4(2)'$ is the [[commutator subgroup|0ASGSTXSBW]] of the [[Ree group|YB62XEQJAC]] ${}^2F_4(2)$.
It has index $2$ in ${}^2F_4(2)$ and its order is
$$17971200 = 2^{11} \cdot 3^3 \cdot 5^2 \cdot 13.$$
It is a finite [[simple group|0YMYMNQ0QZ]], found by Jacques Tits.

## Remarks

The 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.
So the Tits group is not strictly a group of Lie type, and it is not counted among the $26$ [[sporadic groups|PZ49Z4CBFZ]] either.
Some authors list it as a group of Lie type, and others count it as a $27$th sporadic group.

## Explanations

### L1 human

The Tits group is a single finite simple group that sits at the edge of the classification.
It 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.