Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#17985163 |
| Fitting, socle, Hall | C2×C19×C79 ⋊ C3 |
| derived, Hall | C19×C79 ⋊ C2×C3 |
| Hall | C2×C79 ⋊ C19⋊C3 |
| Sylow | C79 ⋊ C2×C19⋊C3 |
| Hall | C2×C19 ⋊ C79⋊C3 |
| Sylow | C19 ⋊ C2×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #17985163 |
| commutator, hypocenter | C19×C79 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C79 | C3 |
| LCS | G ▷ C19×C79 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
1006 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17985163, #31824703, #31824707, … |
| maximal normal subgroup of | C4×#17985163, #31824703, #31824707, … |
| maximal quotient of | C4×#17985163, C22×#17985163, C2×#27214005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 4);