Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D657 |
| unambiguous semidirect product | C9⋊(C25×D73) |
| unambiguous semidirect product | C73⋊(D9×C25) |
| Fitting, Hall | C9×C25×C73 ⋊ C2 |
| derived, Hall | C9×C73 ⋊ C2×C25 |
| Hall | C25×C73 ⋊ D9 |
| Hall | C9×C25 ⋊ D73 |
| Sylow | C73 ⋊ D9×C25 |
| Sylow | C9 ⋊ C25×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D657 |
| commutator, hypocenter | C9×C73 | C2×C25 |
| Frattini | C3×C5 | C5×D219 |
| Fitting | C9×C25×C73 | C2 |
| socle | C3×C5×C73 | C5×D3 |
| prime radical | C5×D657 | C5 |
| cosocle | C5×C9×C73 | C2×C5 |
| LCS | G ▷ C9×C73 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16425 |
8250 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 7);