Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#63454 |
| Fitting | C5×C9×C4⋊C4 ⋊ C2 |
| Hall | C5×C9 ⋊ #117 |
| Sylow | C9 ⋊ C5×#117 |
228 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 720 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2,3,4,5)(6,11,13,12,7,9,8,14,10)(15,16,17,18)(20,24)(21,25);(19,21,22,25)(20,23,24,26);(7,9)(8,12)(10,11)(13,14)(19,20)(21,23)(22,24)(25,26)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 772);