Finite Group DatabasebetaFinite Group Databasebeta| order | 32706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D711 |
| unambiguous semidirect product | C9⋊(C23×D79) |
| unambiguous semidirect product | C79⋊(D9×C23) |
| Fitting, Hall | C9×C23×C79 ⋊ C2 |
| derived, Hall | C9×C79 ⋊ C2×C23 |
| Hall | C23×C79 ⋊ D9 |
| Hall | C9×C23 ⋊ D79 |
| Sylow | C79 ⋊ D9×C23 |
| Sylow | C9 ⋊ C23×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D711 |
| commutator, cosocle, hypocenter | C9×C79 | C2×C23 |
| Frattini | C3 | C23×D237 |
| Fitting | C9×C23×C79 | C2 |
| socle | C3×C23×C79 | D3 |
| LCS | G ▷ C9×C79 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16353 |
8211 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32706, 7);