Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22×C3 |
| direct product | C5×#64138 |
| Fitting | C22×C32×C4×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ #123 |
| Sylow | C32 ⋊ C5×#123 |
468 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 154 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) = 720 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3,4,5)(9,10,11)(13,15)(16,18,19,22)(17,21,20,23);(6,7,8)(17,20)(21,23);(7,8)(10,11)(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4429);