Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8×C9 · Schur multiplier (H2) = C2 |
| direct product | C5×C8×C22⋊C9 |
| unambiguous semidirect product | (C22×C8)⋊(C5×C9) |
| unambiguous semidirect product | (C22×C5×C8)⋊C9 |
| derived | C22 ⋊ C5×C8×C9 |
| Hall | C22×C5×C8 ⋊ C9 |
| Sylow | C22×C8 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C8 | A4 |
| commutator, hypocenter | C22 | C5×C8×C9 |
| Frattini | C3×C4 | C2×C5×A4 |
| Fitting | C22×C3×C5×C8 | C3 |
| socle, prime radical | C23×C3×C5 | C3×C4 |
| cosocle | C22×C3×C4 | C2×C3×C5 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C5×C8 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 360 |
480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 659);