Finite Group DatabasebetaFinite Group Databasebeta| order | 33282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C1849 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C1849 |
| unambiguous semidirect product | C3⋊(D3×C1849) |
| Fitting, Hall | C32×C1849 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C1849 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1849 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C1849 |
| Frattini | C43 | C3⋊D3×C43 |
| Fitting | C32×C1849 | C2 |
| socle, cosocle | C32×C43 | C2×C43 |
| prime radical | C3⋊D3×C43 | C43 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C1849 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16641 |
11094 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33282, 15);