Finite Group DatabasebetaFinite Group Databasebeta| order | 24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#14578512⋊C2 |
| derived, Sylow | C271 ⋊ C2×C5×C9 |
| Hall | C5×#14578512 ⋊ C2 |
| Hall | C5×D271 ⋊ C9 |
| Hall | #14578512 ⋊ C2×C5 |
| Hall | C5×C271 ⋊ C2×C9 |
| Hall | D271 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D271⋊C3 |
| commutator, hypocenter | C271 | C2×C5×C9 |
| Frattini | C3 | C5×D271⋊C3 |
| Fitting, socle | C3×C5×C271 | C2×C3 |
| prime radical | C3×C5×D271 | C3 |
| cosocle | C3×C271 | C2×C3×C5 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12195 |
765 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24390, 15);