Finite Group DatabasebetaFinite Group Databasebeta| order | 32850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C73 · Schur multiplier (H2) = C3 |
| direct product | C73×C3⋊D75 |
| unambiguous semidirect product | C3⋊(C73×D75) |
| unambiguous semidirect product | C25⋊(C3⋊D3×C73) |
| Fitting, Hall | C32×C25×C73 ⋊ C2 |
| derived, Hall | C32×C25 ⋊ C2×C73 |
| Hall | C25×C73 ⋊ C3⋊D3 |
| Hall | C32×C73 ⋊ D25 |
| Sylow | C25 ⋊ C3⋊D3×C73 |
| Sylow | C32 ⋊ D25×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | C3⋊D75 |
| commutator, cosocle, hypocenter | C32×C25 | C2×C73 |
| Frattini | C5 | C73×C3⋊D15 |
| Fitting | C32×C25×C73 | C2 |
| socle | C32×C5×C73 | D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C73 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16425 |
8322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32850, 35);