Fusion systems for groups of order 8: Difference between revisions
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| [[elementary abelian group:E8]] || 5 || 1 || 1 || [[fusion systems for elementary abelian group:E8]] | | [[elementary abelian group:E8]] || 5 || 1 || 1 || [[fusion systems for elementary abelian group:E8]] | ||
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==Information on number of fusion systems== | |||
{{fusion systems facts to check against}} | |||
{| class="sortable" border="1" | |||
! Group !! GAP ID second part !! Hall-Senior number !! [[Nilpotency class]] !! Number of fusion systems (strict counting) !! Number of fusion systems up to isomorphism !! Does the identity functor control strong fusion? (Yes if abelian) | |||
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| [[cyclic group:Z8]] || 1 || 3 || 1 || 1 || 1 || Yes | |||
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| [[direct product of Z4 and Z2]] || 2 || 2 || 1 || 1 || 1 || Yes | |||
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| [[dihedral group:D8]] || 3 || 4 || 2 || 4 || 3 || No | |||
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| [[quaternion group]] || 4 || 5 || 2 || 2 || 2 || Yes | |||
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| [[elementary abelian group:E8]] || 5 || 1 || 1 || 45 || 4 || Yes | |||
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! Total (5 groups) !! -- !! -- !! -- !! 53 !! 11 !! 4 Yes, 1 No | |||
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Revision as of 23:48, 4 May 2012
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 |
Information on number of 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 fusion systems (strict counting) | Number of fusion systems up to isomorphism | Does the identity functor control strong fusion? (Yes if abelian) |
|---|---|---|---|---|---|---|
| cyclic group:Z8 | 1 | 3 | 1 | 1 | 1 | Yes |
| direct product of Z4 and Z2 | 2 | 2 | 1 | 1 | 1 | Yes |
| dihedral group:D8 | 3 | 4 | 2 | 4 | 3 | No |
| quaternion group | 4 | 5 | 2 | 2 | 2 | Yes |
| elementary abelian group:E8 | 5 | 1 | 1 | 45 | 4 | Yes |
| Total (5 groups) | -- | -- | -- | 53 | 11 | 4 Yes, 1 No |