Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#3999 |
| Fitting | C2×C32×C4×C5 ⋊ C4 |
| Hall | C32×C5 ⋊ #99 |
| Sylow | C5 ⋊ C32×#99 |
312 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 96 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 — 2 generators on 19 points:
(1,2,3)(7,8,9,11,10)(12,14,15,19)(13,16,17,18);(4,5,6)(8,9,10,11)(12,13)(14,18,19,16)(15,17)171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2568);