represents the simple Tits group .


TitsGroupT
represents the simple Tits group .
Background & Context
- TitsGroupT[] represents the Tits group
, sometimes also denoted
, which is a group of order
. The default representation of TitsGroupT is as a permutation group on the symbols
having two generators.
- The Tits group was first introduced in the mid-1960s by mathematician Jacques Tits as the (simple) derived subgroup of the (non-simple) Ree group
of Lie type. Because
is not strictly a group of Lie type, it is sometimes regarded as a 27
sporadic simple group. The Tits group can be realized as a maximal subgroup of the Fischer group
. In addition to its default permutation representation, it can be defined in terms of generators and relations as
, where
.
- The usual group theoretic functions may be applied to TitsGroupT[], including GroupOrder, GroupGenerators, GroupElements and so on. A number of precomputed properties of the Tits group are available via FiniteGroupData["Tits","prop"].
- When considered together with the "true" sporadic finite simple groups, TitsGroupT[] is considered a "pariah" even though it occurs as a subquotient of MonsterGroupM (which is the criterion whose failure makes JankoGroupJ1, JankoGroupJ3, JankoGroupJ4, LyonsGroupLy, ONanGroupON and RudvalisGroupRu "pariahs").
See Also
Tech Notes
Related Guides
History
Text
Wolfram Research (2010), TitsGroupT, Wolfram Language function, https://reference.wolfram.com/language/ref/TitsGroupT.html.
CMS
Wolfram Language. 2010. "TitsGroupT." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TitsGroupT.html.
APA
Wolfram Language. (2010). TitsGroupT. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TitsGroupT.html
BibTeX
@misc{reference.wolfram_2025_titsgroupt, author="Wolfram Research", title="{TitsGroupT}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/TitsGroupT.html}", note=[Accessed: 09-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_titsgroupt, organization={Wolfram Research}, title={TitsGroupT}, year={2010}, url={https://reference.wolfram.com/language/ref/TitsGroupT.html}, note=[Accessed: 09-August-2025]}