Finite Group DatabasebetaFinite Group Databasebeta| order | 30666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D807 |
| unambiguous semidirect product | C3⋊(C19×D269) |
| unambiguous semidirect product | C269⋊(D3×C19) |
| Fitting, socle, Hall | C3×C19×C269 ⋊ C2 |
| derived, Hall | C3×C269 ⋊ C2×C19 |
| Hall | C19×C269 ⋊ D3 |
| Sylow | C269 ⋊ D3×C19 |
| Hall | C3×C19 ⋊ D269 |
| Sylow | C3 ⋊ C19×D269 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D807 |
| commutator, cosocle, hypocenter | C3×C269 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C269 | C2 |
| LCS | G ▷ C3×C269 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15333 |
7695 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30666, 7);