Finite Group DatabasebetaFinite Group Databasebeta| order | 14706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C43⋊C3)⋊D19) |
| unambiguous semidirect product | (C43⋊C3)⋊D57 |
| Fitting, socle, derived | C3×C19×C43 ⋊ C2×C3 |
| Hall | C3×C19×C43⋊C3 ⋊ C2 |
| Hall | C19×C43 ⋊ C3×D3 |
| Hall | C3×C43⋊C3 ⋊ D19 |
| Sylow | C43 ⋊ C3×D57 |
| Sylow | C19 ⋊ C3⋊(D43⋊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 |
Polycyclic presentation:
2,3^2,19,43|c^a=c^2,d^a=d^18,e^a=e^42,e^b=e^36489 conjugacy classes — view the full character table.
| maximal subgroup of | D57×D43⋊C3, D19×C3⋊(D43⋊C3), D3×(C43⋊C3)⋊D19, … |
| maximal normal subgroup of | D57×D43⋊C3, D19×C3⋊(D43⋊C3), D3×(C43⋊C3)⋊D19, … |
| maximal quotient of | C3⋊((C43⋊C3)⋊Dic19), C2×C3⋊((C43⋊C3)⋊D19) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14706, 68);