Finite Group DatabasebetaFinite Group Databasebeta| order | 16890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1689 |
| unambiguous semidirect product | C3⋊(C5×D563) |
| unambiguous semidirect product | C563⋊(C5×D3) |
| Fitting, socle, Hall | C3×C5×C563 ⋊ C2 |
| derived, Hall | C3×C563 ⋊ C2×C5 |
| Hall | C5×C563 ⋊ D3 |
| Sylow | C563 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ D563 |
| Sylow | C3 ⋊ C5×D563 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1689 |
| commutator, cosocle, hypocenter | C3×C563 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C563 | C2 |
| LCS | G ▷ C3×C563 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8445 |
4230 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D563, D5×D1689, D15⋊D563, … |
| maximal normal subgroup of | C5×D3×D563, D5×D1689, D15⋊D563, … |
| maximal quotient of | C5×Dic1689, C2×C5×D1689 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16890, 6);