First Janko group
One of the 26 sporadic finite simple groups; order 175560.
The sporadic simple group J₁ identified by the ATLAS standard generators and group record.
Definition sourcesReference properties
Reference scope
This entry establishes the group identity and exact order. Representation links upstream may refer to different fields, characteristics or central extensions; those choices must be checked before reuse. [sources]
Names and aliases
J1
Related objects and maps
- SporadicSporadic classificationThe 26 sporadic finite simple groups
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 sporadic simple group J₁ identified by the ATLAS standard generators and group record.
- ATLAS: First Janko groupHeading and OrderOpen source
- ATLAS: First Janko groupStandard generatorsOpen source
- ATLAS of Finite Group Representations: Sporadic groupsJ₁ entryOpen source
group:sporadic-j1#definitionOrder
175560
group:sporadic-j1#orderSimple
Yes
- ATLAS of Finite Group Representations: Sporadic groupsJ₁ entry in sporadic simple groupsOpen source
group:sporadic-j1#simpleAbelian
No
- Finite simple groups: Lecture 1 — Introduction and alternating groupsCFSG statement, first slideOpen source
group:sporadic-j1#abelianRepresentation coverage
Classification record; follow the ATLAS for available representations.
- ATLAS: First Janko groupRepresentationsOpen source
group:sporadic-j1#representation-scopeReference scope
This entry establishes the group identity and exact order. Representation links upstream may refer to different fields, characteristics or central extensions; those choices must be checked before reuse.
- ATLAS: First Janko groupRepresentations and representation headingsOpen source
group:sporadic-j1#scope-1Sporadic classification
family:finite-sporadic
group:sporadic-j1#relation-1