Endomorphism structure of groups of order 8
This article gives specific information, namely, endomorphism structure, about a family of groups, namely: groups of order 8.
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Automorphism groups
| Group | GAP ID (second part) | Order of automorphism group | Iso. class of automorphism group | Log_2 of largest power of 2 dividing automorphism group order | Iso. class of 2-Sylow subgroup of automorphism group | Log_2 of order of 2-core | Iso. class of 2-core | Log_2 of order of inner automorphism group | Iso. class of inner automorphism group |
|---|---|---|---|---|---|---|---|---|---|
| cyclic group:Z8 | 1 | 4 | Klein four-group | 2 | Klein four-group | 2 | Klein four-group | 0 | trivial group |
| direct product of Z4 and Z2 | 2 | 8 | dihedral group:D8 | 3 | dihedral group:D8 | 3 | dihedral group:D8 | 0 | trivial group |
| dihedral group:D8 | 3 | 8 | dihedral group:D8 | 3 | dihedral group:D8 | 3 | dihedral group:D8 | 2 | Klein four-group |
| quaternion group | 4 | 24 | symmetric group:S4 | 3 | dihedral group:D8 | 2 | Klein four-group | 2 | Klein four-group |
| elementary abelian group:E8 | 5 | 168 | general linear group:GL(3,2) | 3 | dihedral group:D8 | 0 | trivial group | 0 | trivial group |