Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×#63783 |
| Fitting | C32×C5×D4 ⋊ C4 |
| Hall | C32×C5 ⋊ #104 |
| Sylow | C32 ⋊ C5×#104 |
168 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 32 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 — 2 generators on 19 points:
(1,2,3,4,5)(6,8,11)(7,10,9)(12,14)(13,16)(15,18)(17,19);(6,7)(8,10,11,9)(12,13,15,17,16,14,19,18)120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2651);