Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C22 |
| direct product | C2×C9×C24⋊C5 |
| unambiguous semidirect product | (C25×C9)⋊C5 |
| Fitting, Hall | C25×C9 ⋊ C5 |
| derived | C24 ⋊ C2×C5×C9 |
| Sylow | C25 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C24⋊C5 |
| commutator, hypocenter | C24 | C2×C5×C9 |
| Frattini | C3 | C2×C3×C24⋊C5 |
| Fitting | C25×C9 | C5 |
| socle | C25×C3 | C3×C5 |
| prime radical | C2×C3×C24⋊C5 | C3 |
| cosocle | C24×C3 | C2×C3×C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C2×C9 | |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4580);