Fusion systems for groups of order 8
(Redirected from Order 2^3 fusion systems)
This article gives specific information, namely, fusion systems, about a family of groups, namely: groups of order 8.
View fusion systems for group families | View fusion systems for groups of a particular order |View other specific information about groups of order 8
| Group | GAP ID second part | Hall-Senior number | Nilpotency class | Fusion systems page |
|---|---|---|---|---|
| cyclic group:Z8 | 1 | 3 | 1 | fusion systems for cyclic group:Z8 |
| direct product of Z4 and Z2 | 2 | 2 | 1 | fusion systems for direct product of Z4 and Z2 |
| dihedral group:D8 | 3 | 4 | 2 | fusion systems for dihedral group:D8 |
| quaternion group | 4 | 5 | 2 | fusion systems for quaternion group |
| elementary abelian group:E8 | 5 | 1 | 1 | fusion systems for elementary abelian group:E8 |
To view these in a broader perspective, see fusion systems for groups of prime-cube order | fusion systems for groups of order 2^n
Information on number of saturated fusion systems
FACTS TO CHECK AGAINST FOR FUSION SYSTEMS:
For an abelian group of prime power order: identity functor controls strong fusion for saturated fusion system on abelian group|classification of saturated fusion systems on abelian group of prime power order
| Group | GAP ID second part | Hall-Senior number | Nilpotency class | Number of saturated fusion systems (strict counting) | Number of saturated fusion systems up to isomorphism | Is the group resistant? In other words, does the identity functor control strong fusion in every saturated fusion system? (Yes if abelian) | Is it a group of prime power order with no exotic fusion system? |
|---|---|---|---|---|---|---|---|
| cyclic group:Z8 | 1 | 3 | 1 | 1 | 1 | Yes | Yes |
| direct product of Z4 and Z2 | 2 | 2 | 1 | 1 | 1 | Yes | Yes |
| dihedral group:D8 | 3 | 4 | 2 | 4 | 3 | No | Yes |
| quaternion group | 4 | 5 | 2 | 2 | 2 | Yes | Yes |
| elementary abelian group:E8 | 5 | 1 | 1 | 45 | 4 | Yes | Yes |
| Total (5 groups) | -- | -- | -- | 53 | 11 | 4 Yes, 1 No | All Yes |