Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| isoclinism | isoclinic class of D79⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D79⋊C3 |
| unambiguous semidirect product | D79⋊(C3×C19) |
| unambiguous semidirect product | (C79⋊C3)⋊(C2×C19) |
| Fitting, socle, Hall | C19×C79 ⋊ C2×C3 |
| derived, Sylow | C79 ⋊ C2×C3×C19 |
| Hall | C19×C79⋊C3 ⋊ C2 |
| Hall | C19×D79 ⋊ C3 |
| Hall | C79⋊C3 ⋊ C2×C19 |
| Hall | D79 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D79⋊C3 |
| commutator, hypocenter | C79 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C79 | C2×C3 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
361 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D79⋊C3, C2×C19×D79⋊C3, C19⋊C3×D79⋊C3, … |
| maximal normal subgroup of | D19×D79⋊C3, C2×C19×D79⋊C3, C19⋊C3×D79⋊C3, … |
| maximal quotient of | C19×(C79⋊C3)⋊C4, C2×C19×D79⋊C3, C19×D79⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 13);