Math 2.0

Group theory and generalizations Classification of finite simple groups Object

Tits group

Builds on Ree groupsCommutator subgroupSimple groupSporadic group

Description

The Tits group 2F4(2)′{}^2F_4(2)' is the commutator subgroup of the Ree group 2F4(2){}^2F_4(2). It has index 22 in 2F4(2){}^2F_4(2) and its order is 17971200=211⋅33⋅52⋅13.17971200 = 2^{11} \cdot 3^3 \cdot 5^2 \cdot 13. It is a finite simple group, found by Jacques Tits.

Remarks

The groups 2F4(22n+1){}^2F_4(2^{2n+1}) with n≥1n \ge 1 are simple, but 2F4(2){}^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 2626 sporadic groups either. Some authors list it as a group of Lie type, and others count it as a 2727th sporadic group.

Reading path

To understand this page from the ground up, read these 7 pages in order. The foundations come first.

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Commutator subgroup, concept, no evidence levelCommutator subgroupconceptGroup of Lie type, concept, no evidence levelGroup of Lie typeconceptOrder of a group, concept, no evidence levelOrder of a groupconceptSimple group, concept, no evidence levelSimple groupconceptSporadic group, concept, no evidence levelSporadic groupconceptRee groups, object, no evidence levelRee groupsobjectTits group, object, no evidence levelTits groupobject
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Commutator subgroup concept
  2. Group of Lie type concept
  3. Order of a group concept
  4. Simple group concept
  5. Sporadic group concept
  6. Ree groups object
  7. Tits group object

Further reading

  1. Web https://en.wikipedia.org/wiki/Tits_group
About this page
TagWC16TBY3FN
URIm2://WC16TBY3FN
Kindobject
WritingW0 stub
MSC20D06, 20D08
UsesRee groups, Commutator subgroup, Simple group, Sporadic group
Same as
Changed2 November 2026

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