Finite Group DatabasebetaFinite Group Databasebeta| order | 16698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D759 |
| unambiguous semidirect product | C3⋊(C11×D253) |
| unambiguous semidirect product | C11⋊(C11×D69) |
| Fitting, socle, Hall | C3×C112×C23 ⋊ C2 |
| derived | C3×C11×C23 ⋊ C2×C11 |
| Hall | C112×C23 ⋊ D3 |
| Hall | C3×C112 ⋊ D23 |
| Sylow | C112 ⋊ D69 |
| Hall | C3×C23 ⋊ C11×D11 |
| Sylow | C23 ⋊ C11×D33 |
| Sylow | C3 ⋊ C11×D253 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D759 |
| commutator, cosocle, hypocenter | C3×C11×C23 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C23 | C2 |
| LCS | G ▷ C3×C11×C23 | |
| UCS | C1 ◁ C11 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1518 |
4191 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D23×D33, C11×D11×D69, D3×C11×D253, … |
| maximal normal subgroup of | C11×D23×D33, C11×D11×D69, D3×C11×D253, … |
| maximal quotient of | C11×Dic759, C2×C11×D759 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16698, 30);