Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D79 |
| Fitting, socle, derived, Hall | C19×C79 ⋊ C2×C3 |
| Hall | C19⋊C3×C79 ⋊ C2 |
| Hall | C19×D79 ⋊ C3 |
| Sylow | C79 ⋊ C2×C19⋊C3 |
| Sylow | C19 ⋊ C3×D79 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C79 | C2×C3 |
| LCS | G ▷ C19×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
369 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D79, C2×C19⋊C3×D79, #41028282, … |
| maximal normal subgroup of | D19⋊C3×D79, C2×C19⋊C3×D79, #41028282, … |
| maximal quotient of | C19⋊C3×Dic79, C2×C19⋊C3×D79, D79×#4294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 14);