Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D9×C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C22 |
| direct product | D9×C24⋊C5 |
| unambiguous semidirect product | C9⋊(C2×C24⋊C5) |
| unambiguous semidirect product | (C24×D9)⋊C5 |
| Fitting, derived | C24×C9 ⋊ C2×C5 |
| Hall | C24×D9 ⋊ C5 |
| Sylow | C9 ⋊ C2×C24⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C24×C9 | C2×C5 |
| Frattini | C3 | D3×C24⋊C5 |
| socle | C24×C3 | C5×D3 |
| LCS | G ▷ C24×C9 | |
| UCS | C1 | |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4572);