Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C22×C3×C4×C5×D3 |
| Fitting | C22×C32×C4×C5 ⋊ C2 |
| derived | C3 ⋊ C23×C3×C4×C5 |
| Hall | C32×C5 ⋊ C23×C4 |
| Sylow | C32 ⋊ C23×C4×C5 |
998 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×D3×AGL(1,𝔽31), C22×C3×C5×D3×AGL(1,𝔽5) |
| maximal quotient of | C2×C4×D3×AGL(1,𝔽31), C22×C3×C5×D3×AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5776);