Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #3861×Dic57 |
| unambiguous semidirect product | C3⋊(Dic19×#3861) |
| derived | C3×C72×C19 ⋊ C3×C4 |
| Hall | C3×C19×#3861 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Hall | C3×#3861 ⋊ Dic19 |
| Sylow | C72 ⋊ C3×Dic57 |
| Sylow | C19 ⋊ Dic3×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D57×#3861 |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×C19×#3861 | C2 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11172 |
1140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 733);