Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #3744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×#63632 |
| Fitting | C32×C42×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ #104 |
| Sylow | C32 ⋊ C5×#104 |
264 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 94 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 — 3 generators on 19 points:
(1,2,3,4,5)(7,10,11,12)(17,18,19);(6,7)(8,10)(9,11)(12,13)(15,16)(18,19);(14,15,16)390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1364);