Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C32×#4086 |
| Fitting | C2×C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ #127 |
| Sylow | C5 ⋊ C32×#127 |
648 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 222 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)(7,8,10,11,9)(13,15)(17,19);(4,5,6)(16,17,18,19);(8,9)(10,11)(12,13)(14,15)(17,19)306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×#127, C3⋊D3×#4086, #72231582 |
| maximal normal subgroup of | C32×D5×#127, C3⋊D3×#4086, #72231582 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4175);