Finite Group DatabasebetaFinite Group Databasebeta| order | 17138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D451 |
| unambiguous semidirect product | C11⋊(C19×D41) |
| unambiguous semidirect product | C41⋊(C19×D11) |
| Fitting, socle, Hall | C11×C19×C41 ⋊ C2 |
| derived, Hall | C11×C41 ⋊ C2×C19 |
| Hall | C19×C41 ⋊ D11 |
| Hall | C11×C19 ⋊ D41 |
| Sylow | C41 ⋊ C19×D11 |
| Sylow | C11 ⋊ C19×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D451 |
| commutator, cosocle, hypocenter | C11×C41 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C11×C19×C41 | C2 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8569 |
4313 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×D11×D41, D19×D451, D209⋊D41, … |
| maximal normal subgroup of | C19×D11×D41, D19×D451, D209⋊D41, … |
| maximal quotient of | C19×Dic451, C2×C19×D451 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17138, 6);