Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#4029 |
| Fitting | C32×C5×C22⋊C4 ⋊ C2 |
| Hall | C32×C5 ⋊ #123 |
| Sylow | C5 ⋊ C32×#123 |
468 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 720 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(7,8,10,11,9)(13,15)(17,21)(20,23);(4,5,6)(12,13)(14,15)(16,18,19,22)(17,20,21,23);(8,9)(10,11)(16,17)(18,20)(19,21)(22,23)306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4126);