Fusion systems for groups of order 8

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