Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25×C3 |
| direct product | C5×#64366 |
| Fitting | C32×C5×#41 ⋊ C2 |
| Hall | C32×C5 ⋊ H(5,𝔽2) |
| Sylow | C32 ⋊ C5×H(5,𝔽2) |
996 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 306 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 360 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3,4,5)(6,8,9,12)(7,11,10,13)(17,18,19);(7,10)(11,13)(14,15,16);(6,7)(8,11)(9,10)(12,13);(8,12)(11,13)(15,16)(18,19)285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5816);