Finite Group DatabasebetaFinite Group Databasebeta| order | 19836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | #1181×#4296 |
| Fitting, socle, derived, Hall | C19×C29 ⋊ C4×C9 |
| Hall | C29×#4296 ⋊ C4 |
| Hall | C19×#1181 ⋊ C9 |
| Sylow | C29 ⋊ C4×#4296 |
| Sylow | C19 ⋊ C9×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C29 | C4×C9 |
| prime radical, cosocle | C19⋊C3×D29 | C2×C3 |
| LCS | G ▷ C19×C29 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 551 |
121 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19836, 68);