Finite Group DatabasebetaFinite Group Databasebeta| order | 14706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C9)⋊D19 |
| derived, Hall | C19×C43 ⋊ C2×C9 |
| Hall | C19×C43⋊C9 ⋊ C2 |
| Hall | D817 ⋊ C9 |
| Hall | C43⋊C9 ⋊ D19 |
| Sylow | C43 ⋊ C9×D19 |
| Sylow | C19 ⋊ D43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C43⋊C3)⋊D19 |
| commutator, hypocenter | C19×C43 | C2×C9 |
| Fitting, socle, cosocle | C3×C19×C43 | C2×C3 |
| prime radical | C3×D817 | C3 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7353 |
Polycyclic presentation:
2,3,19,43,3|b^3=e,c^a=c^18,d^a=d^42,d^b=d^36498 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D43⋊C9, C2×(C43⋊C9)⋊D19 |
| maximal normal subgroup of | D19×D43⋊C9, C2×(C43⋊C9)⋊D19 |
| maximal quotient of | (C43⋊C9)⋊Dic19, C2×(C43⋊C9)⋊D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14706, 21);