Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C79 · Schur multiplier (H2) = C1 |
| direct product | C3×D19×C79 |
| Fitting, socle, Hall | C3×C19×C79 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C3×C79 |
| Hall | C19×C79 ⋊ C2×C3 |
| Hall | C3×C19 ⋊ C2×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C79 | D19 |
| commutator, hypocenter | C19 | C2×C3×C79 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C79 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C79 | |
16 conjugacy classes of subgroups.
2607 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D19×D79, D3×D19×C79, D19×D237, … |
| maximal normal subgroup of | C3×D19×D79, D3×D19×C79, D19×D237, … |
| maximal quotient of | C3×Dic19×C79, C2×C3×D19×C79, C9×D19×C79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 7);