Finite Group DatabasebetaFinite Group Databasebeta| order | 19074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C17 |
| direct product | C11×C3⋊(C17⋊D17) |
| unambiguous semidirect product | C3⋊(C11×C17⋊D17) |
| unambiguous semidirect product | C17⋊(C11×D51) |
| Fitting, socle, Hall | C3×C11×C172 ⋊ C2 |
| derived, Hall | C3×C172 ⋊ C2×C11 |
| Hall | C11×C172 ⋊ D3 |
| Sylow | C172 ⋊ D3×C11 |
| Hall | C3×C11 ⋊ C17⋊D17 |
| Sylow | C3 ⋊ C11×C17⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊(C17⋊D17) |
| commutator, cosocle, hypocenter | C3×C172 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C172 | C2 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 ◁ C11 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9537 |
4785 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D17×D51, D3×C11×C17⋊D17, D187⋊D51, … |
| maximal normal subgroup of | C11×D17×D51, D3×C11×C17⋊D17, D187⋊D51, … |
| maximal quotient of | C11×C3⋊#11923880, C2×C11×C3⋊(C17⋊D17) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19074, 19);