Finite Group DatabasebetaFinite Group Databasebeta| order | 32766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D127⋊C3 |
| unambiguous semidirect product | D127⋊(C3×C43) |
| unambiguous semidirect product | (C127⋊C3)⋊(C2×C43) |
| Fitting, socle, Hall | C43×C127 ⋊ C2×C3 |
| derived, Sylow | C127 ⋊ C2×C3×C43 |
| Hall | C43×C127⋊C3 ⋊ C2 |
| Hall | C43×D127 ⋊ C3 |
| Hall | C127⋊C3 ⋊ C2×C43 |
| Hall | D127 ⋊ C3×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D127⋊C3 |
| commutator, cosocle, hypocenter | C127 | C2×C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C43×C127 | C2×C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5461 |
1161 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32766, 13);