Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C169⋊C3)⋊D19 |
| Fitting, derived, Hall | C19×C169 ⋊ C2×C3 |
| Hall | C19×C169⋊C3 ⋊ C2 |
| Hall | D3211 ⋊ C3 |
| Hall | C169⋊C3 ⋊ D19 |
| Sylow | C169 ⋊ C3×D19 |
| Sylow | C19 ⋊ D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C19×C169 | C2×C3 |
| Frattini | C13 | (C13⋊C3)⋊D19 |
| socle | C13×C19 | D13⋊C3 |
| LCS | G ▷ C19×C169 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3211 |
Polycyclic presentation:
2,3,13,19,13|c^13=e^12,c^a=c^12e,d^a=d^18,e^a=e^12,c^b=c^9e^12,e^b=e^9565 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D169⋊C3, C2×(C169⋊C3)⋊D19 |
| maximal normal subgroup of | D19×D169⋊C3, C2×(C169⋊C3)⋊D19 |
| maximal quotient of | #50310127, C2×(C169⋊C3)⋊D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 9);