Finite groups · Group

${}^{2}\!F_{4}(2)'$ Tits group

The simple derived subgroup of ²F₄(2), of index two and order 17971200.

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Classification coverageFinite simpleLie-type exceptionClassification

Definition

The commutator subgroup ²F₄(2)′ of the smallest large Ree group.

Definition sources

Order: $17971200$
Center: $1$

Reference properties

Property	Value	Evidence
Order	$17971200$	Sources
Center	$1$	Sources
Simple	Yes	Sources
Abelian	No	Sources
Classification convention	Lie-type small case; excluded from the 26 sporadic groups.	Sources

Identity and representation scope

²F₄(2) itself is not simple. Its simple derived subgroup is the Tits group, and the parent group is its extension by an outer involution. [sources]

This classification record links to available ATLAS representations. It does not assert a complete local list of ordinary complex irreducibles. [sources]

Names and aliases

2F4(2)' · Tits · T

Aliases identify the stated object under this record’s conventions. Type names and broader search terms are kept separate.

Related objects and maps

${}^{2}\!F_{4}(q)$
Large Ree simple groups
Derived small case of ²F₄

Claims and sources

Each assertion has a stable identifier within this record and a source locator or derivation. Cite the dataset edition when referring to a corrected or historical claim.

Definition

The commutator subgroup ²F₄(2)′ of the smallest large Ree group.

Finite simple groups: Lecture 4 — Exceptional groupsSuzuki–Ree small casesOpen source
ATLAS: Tits group ²F₄(2)′Heading and standard generatorsOpen source

group:tits#definition

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Order

17971200

ATLAS: Tits group ²F₄(2)′OrderOpen source

group:tits#order

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Center

1

ATLAS: Tits group ²F₄(2)′Simple group identityOpen source

Derivation: The center of a nonabelian simple group is trivial.

Premises: group:tits#simple · group:tits#abelian

group:tits#center

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Simple

Yes

Finite simple groups: Lecture 4 — Exceptional groupsSuzuki–Ree small casesOpen source

group:tits#simple

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Abelian

No

Finite simple groups: Lecture 4 — Exceptional groupsSimple Tits group of composite orderOpen source

group:tits#abelian

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Classification convention

Lie-type small case; excluded from the 26 sporadic groups.

ATLAS of Finite Group Representations: Sporadic groupsMiscellaneousOpen source
Finite simple groups: Lecture 4 — Exceptional groupsSuzuki–Ree small casesOpen source

group:tits#classification-convention

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Identity and representation scope

²F₄(2) itself is not simple. Its simple derived subgroup is the Tits group, and the parent group is its extension by an outer involution.

ATLAS: Tits group ²F₄(2)′Standard generators of ²F₄(2) = T.2Open source

group:tits#scope-1

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Identity and representation scope

This classification record links to available ATLAS representations. It does not assert a complete local list of ordinary complex irreducibles.

ATLAS: Tits group ²F₄(2)′RepresentationsOpen source

group:tits#scope-2

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Derived small case of ²F₄

family:finite-ree-f4

Finite simple groups: Lecture 4 — Exceptional groupsSuzuki–Ree small casesOpen source

group:tits#relation-1

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