Finite Group DatabasebetaFinite Group Databasebeta| order | 17138 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19×C41 · Schur multiplier (H2) = C1 |
| direct product | C19×D11×C41 |
| unambiguous semidirect product | C11⋊(C2×C19×C41) |
| Fitting, socle, Hall | C11×C19×C41 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C19×C41 |
| Hall | C11×C41 ⋊ C2×C19 |
| Hall | C11×C19 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19×C41 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C19×C41 |
| Frattini | C1 | G |
| Fitting, socle | C11×C19×C41 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C19×C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8569 |
5453 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×D11×D41, D11×D19×C41, D11×D779, … |
| maximal normal subgroup of | C19×D11×D41, D11×D19×C41, D11×D779, … |
| maximal quotient of | C19×C41×Dic11, C2×C19×D11×C41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17138, 5);