Fusion systems for groups of order 2^n
This article gives specific information, namely, fusion systems, about a family of groups, namely: groups of order 2^n.
View fusion systems of group families | View other specific information about groups of order 2^n
This article provides a brief summary of fusion systems for groups of order 2^n. In particular, this provides an approximate description of the 2-local behavior of all finite groups (and more).
Particular cases
| Number of groups of order | Information on groups | Information on fusion systems | ||
|---|---|---|---|---|
| 0 | 1 | 1 | trivial group | nothing to discuss |
| 1 | 2 | 1 | cyclic group:Z2 | the only fusion system is the inner fusion system |
| 2 | 4 | 2 | groups of order 4 | fusion systems for groups of order 4 |
| 3 | 8 | 5 | groups of order 8 | fusion systems for groups of order 8 |
| 4 | 16 | 14 | groups of order 16 | fusion systems for groups of order 16 |
| 5 | 32 | 51 | groups of order 32 | fusion systems for groups of order 32 |
| 6 | 64 | 267 | groups of order 64 | fusion systems for groups of order 64 |
| 7 | 128 | 2328 | groups of order 128 | fusion systems for groups of order 128 |
| 8 | 256 | 56092 | groups of order 256 | fusion systems for groups of order 256 |
| 9 | 512 | 10494213 | groups of order 512 | fusion systems for groups of order 512 |
| 10 | 1024 | 49487367289 | groups of order 1024 | fusion systems for groups of order 1024 |
