Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#4092 |
| Fitting | C2×C32×C5×Q8 ⋊ C2 |
| Hall | C32×C5 ⋊ C22⋊Q8 |
| Sylow | C5 ⋊ C32×C22⋊Q8 |
444 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 210 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)(13,15)(16,18,19,23)(17,20,21,22);(4,5,6)(16,17,19,21)(18,22,23,20);(8,9)(10,11)(12,13)(14,15)306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4188);