Higman–Sims group
One of the 26 sporadic finite simple groups; order 44352000.
The sporadic simple group HS 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
Higman-Sims
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 HS identified by the ATLAS standard generators and group record.
- ATLAS: Higman–Sims groupHeading and OrderOpen source
- ATLAS: Higman–Sims groupStandard generatorsOpen source
- ATLAS of Finite Group Representations: Sporadic groupsHS entryOpen source
group:sporadic-hs#definitionOrder
44352000
group:sporadic-hs#orderSimple
Yes
- ATLAS of Finite Group Representations: Sporadic groupsHS entry in sporadic simple groupsOpen source
group:sporadic-hs#simpleAbelian
No
- Finite simple groups: Lecture 1 — Introduction and alternating groupsCFSG statement, first slideOpen source
group:sporadic-hs#abelianRepresentation coverage
Classification record; follow the ATLAS for available representations.
- ATLAS: Higman–Sims groupRepresentationsOpen source
group:sporadic-hs#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: Higman–Sims groupRepresentations and representation headingsOpen source
group:sporadic-hs#scope-1Sporadic classification
family:finite-sporadic
group:sporadic-hs#relation-1