Finite Group DatabasebetaFinite Group Databasebeta| order | 24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (#14578514⋊C2)⋊C5 |
| unambiguous semidirect product | (#14578514⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C271 ⋊ C2×C5×C9 |
| Hall | #14578514⋊C5 ⋊ C2 |
| Hall | #14578514⋊C2 ⋊ C5 |
| Hall | D271⋊C5 ⋊ C9 |
| Hall | #14578514 ⋊ C2×C5 |
| Hall | C271⋊C5 ⋊ C2×C9 |
| Hall | D271 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C271 | C2×C5×C9 |
| prime radical | (D271⋊C3)⋊C5 | C3 |
| cosocle | C271⋊C3 | C2×C3×C5 |
| LCS | G ▷ C271 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 271 |
Polycyclic presentation:
2,3,5,3,271|b^3=d,e^a=e^270,e^b=e^169,e^c=e^10,e^d=e^2893 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24390, 20);