Finite Group DatabasebetaFinite Group Databasebeta| order | 32706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1817 |
| unambiguous semidirect product | C23⋊(C9×D79) |
| Fitting, Hall | C9×C23×C79 ⋊ C2 |
| derived, Hall | C23×C79 ⋊ C2×C9 |
| Hall | C9×C79 ⋊ D23 |
| Hall | C9×C23 ⋊ D79 |
| Sylow | C79 ⋊ C9×D23 |
| Sylow | C23 ⋊ C9×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1817 |
| commutator, hypocenter | C23×C79 | C2×C9 |
| Frattini | C3 | C3×D1817 |
| Fitting | C9×C23×C79 | C2 |
| socle, cosocle | C3×C23×C79 | C2×C3 |
| prime radical | C3×D1817 | C3 |
| LCS | G ▷ C23×C79 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16353 |
8190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32706, 5);