Finite Group DatabasebetaFinite Group Databasebeta| order | 24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#14578514⋊C2 |
| Fitting, socle, Hall | C5×C271 ⋊ C2×C9 |
| derived, Sylow | C271 ⋊ C2×C5×C9 |
| Hall | C5×#14578514 ⋊ C2 |
| Hall | C5×D271 ⋊ C9 |
| Hall | #14578514 ⋊ C2×C5 |
| Hall | D271 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #14578514⋊C2 |
| commutator, hypocenter | C271 | C2×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C271 | C2×C9 |
| prime radical | C5×D271⋊C3 | C3 |
| cosocle | C271⋊C3 | C2×C3×C5 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1355 |
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24390, 25);