Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D169⋊C3 |
| unambiguous semidirect product | D169⋊(C3×C19) |
| unambiguous semidirect product | (C169⋊C3)⋊(C2×C19) |
| Fitting, Hall | C19×C169 ⋊ C2×C3 |
| derived, Sylow | C169 ⋊ C2×C3×C19 |
| Hall | C19×C169⋊C3 ⋊ C2 |
| Hall | C19×D169 ⋊ C3 |
| Hall | C169⋊C3 ⋊ C2×C19 |
| Hall | D169 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C2×C3×C19 |
| Frattini | C13 | C19×D13⋊C3 |
| Fitting | C19×C169 | C2×C3 |
| socle | C13×C19 | D13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3211 |
646 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#10621721⋊C3, #50310149, D19×D169⋊C3, … |
| maximal normal subgroup of | C19×#10621721⋊C3, #50310149, D19×D169⋊C3, … |
| maximal quotient of | C19×Dic169⋊C3, C2×C19×D169⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 8);