Finite Group DatabasebetaFinite Group Databasebeta| order | 9044 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D133 |
| unambiguous semidirect product | (C7×D17)⋊D19 |
| unambiguous semidirect product | (C19×D17)⋊D7 |
| Fitting, socle, derived, Hall | C7×C17×C19 ⋊ C22 |
| Hall | C17×C19 ⋊ C2×D7 |
| Hall | C7×C19 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×D19 |
| Sylow | C19 ⋊ D7×D17 |
| Sylow | C17 ⋊ C2×D133 |
| Sylow | C7 ⋊ D17×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C17×C19 | C22 |
| LCS | G ▷ C7×C17×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
680 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#11716327, D17×#11716328, D17×ΓL(1,𝔽8)⋊D19, … |
| maximal normal subgroup of | D17×#11716327, D17×#11716328, D17×ΓL(1,𝔽8)⋊D19, … |
| maximal quotient of | C3×D17×D133, D17×D399, D51×D133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9044, 18);