Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#63849 |
| Hall | C32×C5 ⋊ #117 |
| Sylow | C32 ⋊ C5×#117 |
358 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3,4,5)(10,12,13,17)(11,14,15,16)(18,19,20)(21,22,23);(6,8,9,7)(12,17)(14,16)(19,20);(6,7,9,8)(10,11,13,15)(12,16,17,14)(22,23)240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3408);