Finite Group DatabasebetaFinite Group Databasebeta| order | 35730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#16813208⋊C2 |
| unambiguous semidirect product | #16813208⋊(C2×C5) |
| derived, Sylow | C397 ⋊ C2×C5×C9 |
| Hall | C5×#16813208 ⋊ C2 |
| Hall | C5×D397 ⋊ C9 |
| Hall | #16813208 ⋊ C2×C5 |
| Hall | C5×C397 ⋊ C2×C9 |
| Hall | D397 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D397⋊C3 |
| commutator, hypocenter | C397 | C2×C5×C9 |
| Frattini | C3 | C5×D397⋊C3 |
| Fitting, socle | C3×C5×C397 | C2×C3 |
| prime radical | C3×C5×D397 | C3 |
| cosocle | C3×C397 | C2×C3×C5 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17865 |
1080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35730, 10);