Finite Group DatabasebetaFinite Group Databasebeta| order | 19558 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1397 |
| unambiguous semidirect product | C11⋊(C7×D127) |
| Fitting, socle, Hall | C7×C11×C127 ⋊ C2 |
| derived, Hall | C11×C127 ⋊ C2×C7 |
| Hall | C7×C127 ⋊ D11 |
| Sylow | C127 ⋊ C7×D11 |
| Hall | C7×C11 ⋊ D127 |
| Sylow | C11 ⋊ C7×D127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1397 |
| commutator, cosocle, hypocenter | C11×C127 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C127 | C2 |
| LCS | G ▷ C11×C127 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9779 |
4900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19558, 5);