Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C32 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C3⋊C32 |
| unambiguous semidirect product | C3⋊(C3×C5×C32) |
| derived | C3 ⋊ C3×C5×C32 |
| Hall | C32×C5 ⋊ C32 |
| Sylow | C32 ⋊ C5×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C16 | D3 |
| commutator, hypocenter | C3 | C3×C5×C32 |
| Frattini | C16 | C3×C5×D3 |
| Fitting | C32×C5×C16 | C2 |
| socle, prime radical | C2×C32×C5 | C16 |
| cosocle | C3×C16 | C2×C3×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C5×C16 | |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 480 |
720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 218);