Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C5×#64149 |
| Fitting | C2×C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ #127 |
| Sylow | C32 ⋊ C5×#127 |
648 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 720 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3,4,5)(9,10,11)(13,15)(17,19);(6,7,8)(16,17,18,19);(7,8)(10,11)(12,13)(14,15)(17,19)270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×#64149, C5×C3⋊D3×#127, #72231582 |
| maximal normal subgroup of | D5×#64149, C5×C3⋊D3×#127, #72231582 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4433);