Finite Group DatabasebetaFinite Group Databasebeta| order | 9044 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D17×D19 |
| unambiguous semidirect product | (C19×D17)⋊(C2×C7) |
| unambiguous semidirect product | (C17×D19)⋊(C2×C7) |
| unambiguous semidirect product | D323⋊(C2×C7) |
| Fitting, socle, Hall | C7×C17×C19 ⋊ C22 |
| derived, Hall | C17×C19 ⋊ C22×C7 |
| Hall | C7×C19 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×C7×D17 |
| Sylow | C17 ⋊ C2×C7×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D17×D19 |
| commutator, hypocenter | C17×C19 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C19 | C22 |
| LCS | G ▷ C17×C19 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D17×D19⋊C3, D17×#11716321, D17×#11716322, … |
| maximal normal subgroup of | C7×D17×D19⋊C3, D17×#11716321, D17×#11716322, … |
| maximal quotient of | C3×C7×D17×D19, C7×D19×D51, C7×D17×D57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9044, 12);