Finite Group DatabasebetaFinite Group Databasebeta| order | 14706 |
| isoclinism | isoclinic class of D171 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D171 |
| unambiguous semidirect product | C9⋊(D19×C43) |
| unambiguous semidirect product | C19⋊(D9×C43) |
| Fitting, Hall | C9×C19×C43 ⋊ C2 |
| derived, Hall | C9×C19 ⋊ C2×C43 |
| Hall | C19×C43 ⋊ D9 |
| Hall | C9×C43 ⋊ D19 |
| Sylow | C19 ⋊ D9×C43 |
| Sylow | C9 ⋊ D19×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D171 |
| commutator, cosocle, hypocenter | C9×C19 | C2×C43 |
| Frattini | C3 | C43×D57 |
| Fitting | C9×C19×C43 | C2 |
| socle | C3×C19×C43 | D3 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C43 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7353 |
3741 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D171, D9×D19×C43, D171⋊D43, … |
| maximal normal subgroup of | D43×D171, D9×D19×C43, D171⋊D43, … |
| maximal quotient of | C43×Dic171, C2×C43×D171 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14706, 11);