Finite Group DatabasebetaFinite Group Databasebeta| order | 16698 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×D69 |
| unambiguous semidirect product | C3⋊(D23×C121) |
| Fitting, Hall | C3×C23×C121 ⋊ C2 |
| derived, Hall | C3×C23 ⋊ C2×C121 |
| Hall | C23×C121 ⋊ D3 |
| Hall | C3×C121 ⋊ D23 |
| Sylow | C23 ⋊ D3×C121 |
| Sylow | C3 ⋊ D23×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | D69 |
| commutator, hypocenter | C3×C23 | C2×C121 |
| Frattini | C11 | C11×D69 |
| Fitting | C3×C23×C121 | C2 |
| socle, cosocle | C3×C11×C23 | C2×C11 |
| prime radical | C11×D69 | C11 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C121 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8349 |
4356 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D23×C121, D69×D121, D69⋊D121, … |
| maximal normal subgroup of | D3×D23×C121, D69×D121, D69⋊D121, … |
| maximal quotient of | C121×Dic69, C2×C121×D69 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16698, 10);