Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C32×#4021 |
| Fitting | C32×C42×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ #124 |
| Sylow | C5 ⋊ C32×#124 |
456 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 198 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)(7,8,10,11,9)(12,14,15,13)(17,21)(20,23);(4,5,6)(12,13,15,14)(16,18,19,22)(17,20,21,23);(8,9)(10,11)(13,14)(16,17)(18,20)(19,21)(22,23)414 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4117);