Finite Group DatabasebetaFinite Group Databasebeta| order | 8566 |
| automorphism | Aut(G) order 18339806 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4283 |
| unambiguous semidirect product | C4283⋊C2 |
| Fitting, socle, derived, Sylow | C4283 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4283 | C2 |
| LCS | G ▷ C4283 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4283|b^a=b^42822143 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4283, C3×D4283, D12849 |
| maximal normal subgroup of | C2×D4283, C3×D4283 |
| maximal quotient of | Dic4283, C2×D4283, C3×D4283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8566, 1);