Finite Group DatabasebetaFinite Group Databasebeta| order | 24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(D271⋊C5) |
| unambiguous semidirect product | (C271⋊C5)⋊D9 |
| unambiguous semidirect product | D2439⋊C5 |
| Fitting, derived, Hall | C9×C271 ⋊ C2×C5 |
| Hall | C9×C271⋊C5 ⋊ C2 |
| Hall | D2439 ⋊ C5 |
| Hall | C271⋊C5 ⋊ D9 |
| Sylow | C271 ⋊ C5×D9 |
| Sylow | C9 ⋊ D271⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C271 | C2×C5 |
| Frattini | C3 | C3⋊(D271⋊C5) |
| socle | C3×C271 | C5×D3 |
| LCS | G ▷ C9×C271 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2439 |
Polycyclic presentation:
2,3,5,271,3|b^3=e^2,b^a=b^2e,d^a=d^270,e^a=e^2,d^c=d^10273 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24390, 14);