Finite Group DatabasebetaFinite Group Databasebeta| order | 14706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D3×#14578576 |
| unambiguous semidirect product | C3⋊(C2×#14578576) |
| Fitting, socle, derived | C3×C19×C43 ⋊ C2×C3 |
| Hall | C3×#14578576 ⋊ C2 |
| Hall | C19×C43 ⋊ C3×D3 |
| Sylow | C43 ⋊ D3×C19⋊C3 |
| Sylow | C19 ⋊ D3×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C43 | C2×C3 |
| LCS | G ▷ C3×C19×C43 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2451 |
825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#19096733, D3×#19096729, D3×#19096725, … |
| maximal normal subgroup of | D3×#19096733, D3×#19096729, D3×#19096725, … |
| maximal quotient of | Dic3×#14578576, C2×D3×#14578576 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14706, 65);