Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#63729 |
| Hall | C32×C5 ⋊ #102 |
| Sylow | C32 ⋊ C5×#102 |
176 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 34 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) = 120 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3,4,5)(6,8)(7,10,11)(12,13,15,18,16,19,14,17);(6,7)(8,11)(9,10)(13,17)(14,15)(18,19)135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1874);