Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3211 |
| Fitting, Hall | C3×C19×C169 ⋊ C2 |
| derived, Hall | C19×C169 ⋊ C2×C3 |
| Hall | C3×C169 ⋊ D19 |
| Sylow | C169 ⋊ C3×D19 |
| Hall | C3×C19 ⋊ D169 |
| Sylow | C19 ⋊ C3×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3211 |
| commutator, cosocle, hypocenter | C19×C169 | C2×C3 |
| Frattini | C13 | C3×D247 |
| Fitting | C3×C19×C169 | C2 |
| socle | C3×C13×C19 | D13 |
| LCS | G ▷ C19×C169 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9633 |
4821 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D19×D169, D3×D3211, D57⋊D169, … |
| maximal normal subgroup of | C3×D19×D169, D3×D3211, D57⋊D169, … |
| maximal quotient of | C3×Dic3211, C2×C3×D3211 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 20);