Finite Group DatabasebetaFinite Group Databasebeta| order | 35730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(#16813210⋊C2) |
| unambiguous semidirect product | #16813210⋊D5 |
| Fitting, socle, derived, Hall | C5×C397 ⋊ C2×C9 |
| Hall | C5×#16813210 ⋊ C2 |
| Hall | D1985 ⋊ C9 |
| Hall | #16813210 ⋊ D5 |
| Sylow | C397 ⋊ C9×D5 |
| Sylow | C5 ⋊ #16813210⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C397 | C2×C9 |
| prime radical | C5⋊(D397⋊C3) | C3 |
| cosocle | C5×C397⋊C3 | C2×C3 |
| LCS | G ▷ C5×C397 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1985 |
Polycyclic presentation:
2,3^2,5,397|b^3=c,d^a=d^4,e^a=e^396,e^b=e^312,e^c=e^34146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35730, 15);