Finite Group DatabasebetaFinite Group Databasebeta| order | 32706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D23×C79⋊C9 |
| unambiguous semidirect product | C23⋊(C2×C79⋊C9) |
| unambiguous semidirect product | (D23×C79)⋊C9 |
| derived, Hall | C23×C79 ⋊ C2×C9 |
| Hall | C23×C79⋊C9 ⋊ C2 |
| Hall | D23×C79 ⋊ C9 |
| Sylow | C79 ⋊ C9×D23 |
| Sylow | C23 ⋊ C2×C79⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D23×C79⋊C3 |
| commutator, hypocenter | C23×C79 | C2×C9 |
| Fitting, socle, cosocle | C3×C23×C79 | C2×C3 |
| prime radical | C3×D23×C79 | C3 |
| LCS | G ▷ C23×C79 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16353 |
1131 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32706, 11);