Finite Group DatabasebetaFinite Group Databasebeta| order | 8874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1479 |
| unambiguous semidirect product | C3⋊(C3×D493) |
| unambiguous semidirect product | C17⋊(C3×D87) |
| unambiguous semidirect product | C29⋊(C3×D51) |
| Fitting, socle, Hall | C32×C17×C29 ⋊ C2 |
| derived | C3×C17×C29 ⋊ C2×C3 |
| Hall | C17×C29 ⋊ C3×D3 |
| Hall | C32×C29 ⋊ D17 |
| Hall | C32×C17 ⋊ D29 |
| Sylow | C29 ⋊ C3×D51 |
| Sylow | C17 ⋊ C3×D87 |
| Sylow | C32 ⋊ D493 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1479 |
| commutator, hypocenter | C3×C17×C29 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C29 | C2 |
| LCS | G ▷ C3×C17×C29 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
2223 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D29×D51, C3×D17×D87, C3×D3×D493, … |
| maximal normal subgroup of | C3×D29×D51, C3×D17×D87, C3×D3×D493, … |
| maximal quotient of | C3×Dic1479, C2×C3×D1479 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8874, 16);