Finite Group DatabasebetaFinite Group Databasebeta| order | 33282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C43 |
| direct product | C3×C3⋊(C43⋊D43) |
| unambiguous semidirect product | C3⋊(C3×C43⋊D43) |
| Fitting, socle, Hall | C32×C432 ⋊ C2 |
| derived | C3×C432 ⋊ C2×C3 |
| Sylow | C432 ⋊ C3×D3 |
| Sylow | C32 ⋊ C43⋊D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C43⋊D43) |
| commutator, cosocle, hypocenter | C3×C432 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C432 | C2 |
| LCS | G ▷ C3×C432 | |
| UCS | C1 ◁ C3 | |
414 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11094 |
8325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33282, 65);