Finite Group DatabasebetaFinite Group Databasebeta| order | 35730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(#16813208⋊C2) |
| unambiguous semidirect product | #16813208⋊D5 |
| derived, Hall | C5×C397 ⋊ C2×C9 |
| Hall | C5×#16813208 ⋊ C2 |
| Hall | D1985 ⋊ C9 |
| Hall | #16813208 ⋊ D5 |
| Sylow | C397 ⋊ C9×D5 |
| Sylow | C5 ⋊ #16813208⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(D397⋊C3) |
| commutator, hypocenter | C5×C397 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C397 | C2×C3 |
| prime radical | C3×D1985 | C3 |
| LCS | G ▷ C5×C397 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17865 |
Polycyclic presentation:
2,3,5,397,3|b^3=e,c^a=c^4,d^a=d^396,d^b=d^3621026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35730, 12);