Finite Group DatabasebetaFinite Group Databasebeta| order | 19074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D561 |
| unambiguous semidirect product | C3⋊(C17×D187) |
| unambiguous semidirect product | C11⋊(C17×D51) |
| unambiguous semidirect product | C17⋊(C17×D33) |
| Fitting, socle, Hall | C3×C11×C172 ⋊ C2 |
| derived | C3×C11×C17 ⋊ C2×C17 |
| Hall | C11×C172 ⋊ D3 |
| Hall | C3×C172 ⋊ D11 |
| Sylow | C172 ⋊ D33 |
| Hall | C3×C11 ⋊ C17×D17 |
| Sylow | C11 ⋊ C17×D51 |
| Sylow | C3 ⋊ C17×D187 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D561 |
| commutator, cosocle, hypocenter | C3×C11×C17 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C172 | C2 |
| LCS | G ▷ C3×C11×C17 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1122 |
4794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D17×D33, D17×D561, #50302360, … |
| maximal normal subgroup of | C17×D17×D33, D17×D561, #50302360, … |
| maximal quotient of | C17×Dic561, C2×C17×D561 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19074, 17);