Finite Group DatabasebetaFinite Group Databasebeta| order | 35730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D5×#16813210 |
| unambiguous semidirect product | C5⋊(C2×#16813210) |
| Fitting, socle, derived, Hall | C5×C397 ⋊ C2×C9 |
| Hall | C5×#16813210 ⋊ C2 |
| Hall | D5×C397 ⋊ C9 |
| Sylow | C397 ⋊ C9×D5 |
| Sylow | C5 ⋊ C2×#16813210 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C397 | C2×C9 |
| prime radical | D5×C397⋊C3 | C3 |
| cosocle | C5×C397⋊C3 | C2×C3 |
| LCS | G ▷ C5×C397 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1985 |
212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35730, 16);