Endomorphism structure of elementary abelian group:E8
This article gives specific information, namely, endomorphism structure, about a particular group, namely: elementary abelian group:E8.
View endomorphism structure of particular groups | View other specific information about elementary abelian group:E8
This article describes the structure of endomorphisms (and in particular automorphisms) of elementary abelian group:E8, which is the elementary abelian group of order 8, or equivalently, the direct product of three copies of cyclic group:Z2.
Summary of information
| Construct | Value | Order | Second part of GAP ID (if applicable) |
|---|---|---|---|
| endomorphism ring | matrix ring : matrices over field:F2 | 512 | -- |
| automorphism group | projective special linear group:PSL(3,2) (which is the same as ) | 168 | 42 |
| inner automorphism group | trivial group | 1 | 1 |
| outer automorphism group | projective special linear group:PSL(3,2) | 168 | 42 |
| extended automorphism group | projective special linear group:PSL(3,2) | 168 | 42 |
| quasiautomorphism group | projective special linear group:PSL(3,2) | 168 | 42 |
| 1-automorphism group | symmetric group:S7 | 5040 | -- (order too large) |
