Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C13 |
| direct product | C19×C3⋊(C13⋊D13) |
| unambiguous semidirect product | C3⋊(C19×C13⋊D13) |
| unambiguous semidirect product | C13⋊(C19×D39) |
| Fitting, socle, Hall | C3×C132×C19 ⋊ C2 |
| derived, Hall | C3×C132 ⋊ C2×C19 |
| Hall | C132×C19 ⋊ D3 |
| Sylow | C132 ⋊ D3×C19 |
| Hall | C3×C19 ⋊ C13⋊D13 |
| Sylow | C3 ⋊ C19×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C3⋊(C13⋊D13) |
| commutator, cosocle, hypocenter | C3×C132 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132×C19 | C2 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 ◁ C19 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9633 |
4845 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×D13×D39, D247⋊D39, D19×C3⋊(C13⋊D13), … |
| maximal normal subgroup of | C19×D13×D39, D247⋊D39, D19×C3⋊(C13⋊D13), … |
| maximal quotient of | C19×C3⋊#10621725, C2×C19×C3⋊(C13⋊D13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 91);