Finite Group DatabasebetaFinite Group Databasebeta| order | 19074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3179 |
| unambiguous semidirect product | C11⋊(C3×D289) |
| unambiguous semidirect product | C289⋊(C3×D11) |
| Fitting, Hall | C3×C11×C289 ⋊ C2 |
| derived, Hall | C11×C289 ⋊ C2×C3 |
| Hall | C3×C289 ⋊ D11 |
| Sylow | C289 ⋊ C3×D11 |
| Hall | C3×C11 ⋊ D289 |
| Sylow | C11 ⋊ C3×D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3179 |
| commutator, cosocle, hypocenter | C11×C289 | C2×C3 |
| Frattini | C17 | C3×D187 |
| Fitting | C3×C11×C289 | C2 |
| socle | C3×C11×C17 | D17 |
| LCS | G ▷ C11×C289 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9537 |
4773 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D289, D3×D3179, D33⋊D289, … |
| maximal normal subgroup of | C3×D11×D289, D3×D3179, D33⋊D289, … |
| maximal quotient of | C3×Dic3179, C2×C3×D3179 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19074, 4);