Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C32×#4144 |
| Fitting | C2×C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ H(5,𝔽2) |
| Sylow | C5 ⋊ C32×H(5,𝔽2) |
996 conjugacy classes of subgroups; only the 510 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 510 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 360 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(7,8,10,11,9)(13,17)(16,19);(4,5,6)(14,18)(16,19);(12,14)(13,16)(15,18)(17,19);(8,9)(10,11)(12,13)(14,16)(15,17)(18,19)333 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5766);