Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#3964 |
| Hall | C32×C5 ⋊ #102 |
| Sylow | C5 ⋊ C32×#102 |
300 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 150 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 — 2 generators on 23 points:
(1,2,3)(7,8,10,11,9)(17,20)(18,23)(21,22);(4,5,6)(8,9)(10,11)(12,13,14,15)(16,17)(18,20)(19,22)(21,23)306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1269);