Finite Group DatabasebetaFinite Group Databasebeta| order | 19242 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3207 |
| unambiguous semidirect product | C3⋊(C3×D1069) |
| Fitting, socle, Hall | C32×C1069 ⋊ C2 |
| derived | C3×C1069 ⋊ C2×C3 |
| Sylow | C1069 ⋊ C3×D3 |
| Sylow | C32 ⋊ D1069 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3207 |
| commutator, cosocle, hypocenter | C3×C1069 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C1069 | C2 |
| LCS | G ▷ C3×C1069 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6414 |
4815 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D1069, D3×D3207, (C3⋊D3)⋊D1069, … |
| maximal normal subgroup of | C3×D3×D1069, D3×D3207, (C3⋊D3)⋊D1069, … |
| maximal quotient of | C3×Dic3207, C2×C3×D3207 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19242, 14);