Finite Group DatabasebetaFinite Group Databasebeta| order | 24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C271 ⋊ C2×C3×C5 |
| derived, Sylow | C271 ⋊ C2×C32×C5 |
| Hall | C3×(C271⋊C3)⋊C5 ⋊ C2 |
| Hall | C3×D271⋊C3 ⋊ C5 |
| Hall | D271⋊C5 ⋊ C32 |
| Hall | C3×C271⋊C3 ⋊ C2×C5 |
| Hall | C271⋊C5 ⋊ C2×C32 |
| Hall | D271 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (D271⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C271 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C271 | C2×C3×C5 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 813 |
117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24390, 22);