Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×2−1+4⋊C5 |
| unambiguous semidirect product | (C9×2−1+4)⋊C5 |
| Fitting, Hall | C9×2−1+4 ⋊ C5 |
| derived, Sylow | 2−1+4 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C24⋊C5 |
| commutator, hypocenter | 2−1+4 | C5×C9 |
| Frattini, socle | C2×C3 | C3×C24⋊C5 |
| Fitting | C9×2−1+4 | C5 |
| prime radical | C3×2−1+4⋊C5 | C3 |
| cosocle | C3×2−1+4 | C3×C5 |
| LCS | G ▷ 2−1+4 | |
| UCS | C1 ◁ C2×C9 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1542);