Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C32 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#3926 |
| unambiguous semidirect product | C3⋊(C3×#3926) |
| derived | C3×C5 ⋊ C3×C32 |
| Hall | C32×C5 ⋊ C32 |
| Sylow | C32 ⋊ #3926 |
| Sylow | C5 ⋊ C3×C3⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C16 | D15 |
| commutator, hypocenter | C3×C5 | C3×C32 |
| Frattini | C16 | C3×D15 |
| Fitting | C32×C5×C16 | C2 |
| socle, prime radical | C2×C32×C5 | C16 |
| cosocle | C3×C5×C16 | C2×C3 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C3×C16 | |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 480 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 219);