Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C5×#64086 |
| Hall | C32×C5 ⋊ #117 |
| Sylow | C32 ⋊ C5×#117 |
456 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 170 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)(6,7,8,9)(12,16)(14,17)(21,22,23);(10,12)(11,14)(13,16)(15,17)(18,19,20);(10,11,13,15)(12,14,16,17)(19,20)(22,23)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4377);