Finite Group DatabasebetaFinite Group Databasebeta| order | 19074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C17 · Schur multiplier (H2) = C1 |
| direct product | C11×C17×D51 |
| unambiguous semidirect product | C3⋊(C11×C17×D17) |
| unambiguous semidirect product | C17⋊(D3×C11×C17) |
| Fitting, socle, Hall | C3×C11×C172 ⋊ C2 |
| derived | C3×C17 ⋊ C2×C11×C17 |
| Hall | C11×C172 ⋊ D3 |
| Hall | C3×C172 ⋊ C2×C11 |
| Sylow | C172 ⋊ D3×C11 |
| Hall | C3×C11 ⋊ C17×D17 |
| Sylow | C3 ⋊ C11×C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C17 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C11×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C172 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C11×C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1122 |
5049 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C11×C17×D17, C11×D17×D51, C11×D51⋊D17, … |
| maximal normal subgroup of | D3×C11×C17×D17, C11×D17×D51, C11×D51⋊D17, … |
| maximal quotient of | C11×C17×Dic51, C2×C11×C17×D51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19074, 20);