Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22×C3 |
| direct product | C5×#64141 |
| Fitting | C2×C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C32 ⋊ C5×AGL(1,ℤ/8) |
408 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 360 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3,4,5)(7,12)(8,9)(11,13)(17,18,19);(6,8,10,9)(7,11,13,12)(14,15,16);(6,7)(8,11)(9,12)(10,13)(15,16)(18,19)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4437);