Finite Group DatabasebetaFinite Group Databasebeta| order | 19836 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×(C19⋊C3)⋊#1181 |
| unambiguous semidirect product | (C19⋊C3)⋊(C3×#1181) |
| unambiguous semidirect product | (C19⋊#1181)⋊C32 |
| unambiguous semidirect product | (C3×C19⋊#1181)⋊C3 |
| Fitting, socle | C3×C19×C29 ⋊ C3×C4 |
| derived, Hall | C19×C29 ⋊ C32×C4 |
| Hall | C3×C29×C19⋊C3 ⋊ C4 |
| Hall | C19⋊#1181 ⋊ C32 |
| Hall | C3×C19⋊C3 ⋊ #1181 |
| Sylow | C29 ⋊ C3×(C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C32×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C19⋊C3)⋊#1181 |
| commutator, hypocenter | C19×C29 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C29 | C3×C4 |
| prime radical | C3×C19⋊C3×D29 | C2 |
| cosocle | C19×D29 | C2×C32 |
| LCS | G ▷ C19×C29 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1653 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19836, 72);