Finite Group DatabasebetaFinite Group Databasebeta| order | 17138 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C19 · Schur multiplier (H2) = C1 |
| direct product | C11×C19×D41 |
| unambiguous semidirect product | C41⋊(C2×C11×C19) |
| Fitting, socle, Hall | C11×C19×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C11×C19 |
| Hall | C19×C41 ⋊ C2×C11 |
| Hall | C11×C41 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C19 | D41 |
| commutator, cosocle, hypocenter | C41 | C2×C11×C19 |
| Frattini | C1 | G |
| Fitting, socle | C11×C19×C41 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C11×C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8569 |
4598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C19×#4223, C11×C19⋊#4223, C11×D19×D41, … |
| maximal normal subgroup of | C11×C19×#4223, C11×C19⋊#4223, C11×D19×D41, … |
| maximal quotient of | C11×C19×Dic41, C2×C11×C19×D41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17138, 2);