Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#4060 |
| Fitting | C5×C9×SD16 ⋊ C2 |
| Hall | C5×C9 ⋊ AGL(1,ℤ/8) |
| Sylow | C5 ⋊ C9×AGL(1,ℤ/8) |
204 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 360 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3,4,5,6,7,8,9)(10,11,13,14,12)(15,16,18,19)(17,22,21,20);(16,20)(17,21)(19,22);(11,12)(13,14)(16,19)(20,22)225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 707);