Elementary abelian group:E8
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Definition
The elementary abelian group of order eight is defined as followed:
- It is the elementary abelian group of order eight.
- It is the additive group of a three-dimensional vector space over a field of two elements.
- It is the only abelian group of order eight and exponent two.
- It is the generalized dihedral group corresponding to the Klein four-group.
Arithmetic functions
| Function | Value | Explanation |
|---|---|---|
| order | 8 | |
| exponent | 2 | |
| nilpotency class | 1 | |
| derived length | 1 | |
| subgroup rank | 3 | |
| minimum size of generating set | 3 | |
| max-length | 3 | |
| rank | 3 | |
| normal rank | 3 | |
| characteristic rank | 3 | |
| number of subgroups | 16 | |
| number of conjugacy classes | 8 |