Finite Group DatabasebetaFinite Group Databasebeta| order | 19558 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D127⋊C7 |
| unambiguous semidirect product | D127⋊(C7×C11) |
| unambiguous semidirect product | (C127⋊C7)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D127)⋊C7 |
| Fitting, socle, Hall | C11×C127 ⋊ C2×C7 |
| derived, Sylow | C127 ⋊ C2×C7×C11 |
| Hall | C11×C127⋊C7 ⋊ C2 |
| Hall | C11×D127 ⋊ C7 |
| Hall | C127⋊C7 ⋊ C2×C11 |
| Hall | D127 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D127⋊C7 |
| commutator, cosocle, hypocenter | C127 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C127 | C2×C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1397 |
253 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19558, 10);