Finite Group DatabasebetaFinite Group Databasebeta| order | 19836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4294⋊#1181 |
| derived, Hall | C19×C29 ⋊ C4×C9 |
| Hall | C29×#4294 ⋊ C4 |
| Hall | C19⋊#1181 ⋊ C9 |
| Hall | #4294 ⋊ #1181 |
| Sylow | C29 ⋊ #4294⋊C4 |
| Sylow | C19 ⋊ C9×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C19⋊C3)⋊#1181 |
| commutator, hypocenter | C19×C29 | C4×C9 |
| Fitting, socle | C3×C19×C29 | C3×C4 |
| prime radical, cosocle | C3×C19×D29 | C2×C3 |
| LCS | G ▷ C19×C29 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4959 |
Polycyclic presentation:
2,3,2,19,29,3|a^2=c,b^3=f,d^a=d^18,e^a=e^17,d^b=d^7,e^c=e^28243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19836, 14);