Finite Group DatabasebetaFinite Group Databasebeta| order | 14706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C3 |
| direct product | C19×C3⋊D129 |
| unambiguous semidirect product | C3⋊(C19×D129) |
| unambiguous semidirect product | C43⋊(C3⋊D3×C19) |
| Fitting, socle, Hall | C32×C19×C43 ⋊ C2 |
| derived, Hall | C32×C43 ⋊ C2×C19 |
| Hall | C19×C43 ⋊ C3⋊D3 |
| Hall | C32×C19 ⋊ D43 |
| Sylow | C43 ⋊ C3⋊D3×C19 |
| Sylow | C32 ⋊ C19×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C3⋊D129 |
| commutator, cosocle, hypocenter | C32×C43 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19×C43 | C2 |
| LCS | G ▷ C32×C43 | |
| UCS | C1 ◁ C19 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7353 |
3705 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C19×D129, D57⋊D129, C3⋊D3×C19×D43, … |
| maximal normal subgroup of | D3×C19×D129, D57⋊D129, C3⋊D3×C19×D43, … |
| maximal quotient of | C19×C3⋊Dic129, C2×C19×C3⋊D129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14706, 76);