Finite Group DatabasebetaFinite Group Databasebeta| order | 19836 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle | C2×C3×C19×C29 ⋊ C2×C3 |
| derived, Hall | C19×C29 ⋊ C22×C32 |
| Hall | C3×C29×C19⋊C3 ⋊ C22 |
| Hall | C2×D551 ⋊ C32 |
| Hall | C3×C19⋊C3 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C3×D19⋊C3 |
| Sylow | C19 ⋊ C2×C32×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C29⋊(D19⋊C3) |
| commutator, cosocle, hypocenter | C19×C29 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C19×C29 | C2×C3 |
| LCS | G ▷ C19×C29 | |
| UCS | C1 ◁ C2×C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3306 |
810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19836, 87);