Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#63365 |
| Fitting | C5×C9×C22⋊C4 ⋊ C2 |
| Hall | C5×C9 ⋊ #99 |
| Sylow | C9 ⋊ C5×#99 |
156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 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 — 2 generators on 22 points:
(1,2,3,4,5)(6,11,13,12,7,9,8,14,10)(15,17)(16,19,20,21)(18,22);(7,9)(8,12)(10,11)(13,14)(15,16)(17,21)(18,20)(19,22)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 125);