Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| isoclinism | isoclinic class of D237 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D237 |
| unambiguous semidirect product | C3⋊(C19×D79) |
| unambiguous semidirect product | C79⋊(D3×C19) |
| Fitting, socle, Hall | C3×C19×C79 ⋊ C2 |
| derived, Hall | C3×C79 ⋊ C2×C19 |
| Hall | C19×C79 ⋊ D3 |
| Sylow | C79 ⋊ D3×C19 |
| Hall | C3×C19 ⋊ D79 |
| Sylow | C3 ⋊ C19×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D237 |
| commutator, hypocenter | C3×C79 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C79 | C2 |
| LCS | G ▷ C3×C79 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
2280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C19×D79, D19×D237, D57⋊D79, … |
| maximal normal subgroup of | D3×C19×D79, D19×D237, D57⋊D79, … |
| maximal quotient of | C19×Dic237, C2×C19×D237, C19×D711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 10);