Finite Group DatabasebetaFinite Group Databasebeta| order | 8466 |
| automorphism | Aut(G) order 11107392 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4233 |
| unambiguous semidirect product | C3⋊D1411 |
| unambiguous semidirect product | C17⋊D249 |
| unambiguous semidirect product | C83⋊D51 |
| Fitting, socle, derived, Hall | C3×C17×C83 ⋊ C2 |
| Hall | C17×C83 ⋊ D3 |
| Hall | C3×C83 ⋊ D17 |
| Sylow | C83 ⋊ D51 |
| Hall | C3×C17 ⋊ D83 |
| Sylow | C17 ⋊ D249 |
| Sylow | C3 ⋊ D1411 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C83 | C2 |
| LCS | G ▷ C3×C17×C83 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,83|b^a=b^2,c^a=c^16,d^a=d^822118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D83, D17×D249, D3×D1411, … |
| maximal normal subgroup of | D51×D83, D17×D249, D3×D1411, … |
| maximal quotient of | Dic4233, C2×D4233, D12699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8466, 8);