Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#63939 |
| Fitting | C32×C5×Q8 ⋊ C22 |
| Hall | C32×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C32 ⋊ C5×AGL(1,ℤ/8) |
292 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 240 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3,4,5)(6,7,9,10)(8,13,12,11)(14,15,16)(17,18,19);(7,11)(8,12)(10,13)(15,16);(7,10)(11,13)(18,19)165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3528);