Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C169 · Schur multiplier (H2) = C1 |
| direct product | D19⋊C3×C169 |
| unambiguous semidirect product | D19⋊(C3×C169) |
| unambiguous semidirect product | (C19⋊C3)⋊(C2×C169) |
| Fitting, Hall | C19×C169 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C2×C3×C169 |
| Hall | C19⋊C3×C169 ⋊ C2 |
| Hall | D19×C169 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C2×C169 |
| Hall | D19 ⋊ C3×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C3×C169 |
| Frattini | C13 | C13×D19⋊C3 |
| Fitting | C19×C169 | C2×C3 |
| socle, cosocle | C13×C19 | C2×C3×C13 |
| prime radical | C13×D19⋊C3 | C13 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C169 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3211 |
1521 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19⋊C3×D169, C2×D19⋊C3×C169 |
| maximal normal subgroup of | D19⋊C3×D169, C2×D19⋊C3×C169 |
| maximal quotient of | C169×(C19⋊C3)⋊C4, C2×D19⋊C3×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 2);