Finite Group DatabasebetaFinite Group Databasebeta| order | 19074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×D289 |
| unambiguous semidirect product | C289⋊(C2×C3×C11) |
| Fitting, Hall | C3×C11×C289 ⋊ C2 |
| derived, Sylow | C289 ⋊ C2×C3×C11 |
| Hall | C11×C289 ⋊ C2×C3 |
| Hall | C3×C289 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | D289 |
| commutator, cosocle, hypocenter | C289 | C2×C3×C11 |
| Frattini | C17 | C3×C11×D17 |
| Fitting | C3×C11×C289 | C2 |
| socle | C3×C11×C17 | D17 |
| LCS | G ▷ C289 | |
| UCS | C1 ◁ C3×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9537 |
4818 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×#11923876, C3×C11⋊#11923876, C3×D11×D289, … |
| maximal normal subgroup of | C3×C11×#11923876, C3×C11⋊#11923876, C3×D11×D289, … |
| maximal quotient of | C3×C11×Dic289, C2×C3×C11×D289 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19074, 2);