Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1073 |
| unambiguous semidirect product | C29⋊(C9×D37) |
| Fitting, Hall | C9×C29×C37 ⋊ C2 |
| derived, Hall | C29×C37 ⋊ C2×C9 |
| Hall | C9×C37 ⋊ D29 |
| Hall | C9×C29 ⋊ D37 |
| Sylow | C37 ⋊ C9×D29 |
| Sylow | C29 ⋊ C9×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1073 |
| commutator, hypocenter | C29×C37 | C2×C9 |
| Frattini | C3 | C3×D1073 |
| Fitting | C9×C29×C37 | C2 |
| socle, cosocle | C3×C29×C37 | C2×C3 |
| prime radical | C3×D1073 | C3 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9657 |
4842 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#16864280, C9×#16864281, C9×D29×D37, … |
| maximal normal subgroup of | C9×#16864280, C9×#16864281, C9×D29×D37, … |
| maximal quotient of | C9×Dic1073, C2×C9×D1073 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 5);