Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C32×#4028 |
| Fitting | C32×C5×C22⋊C4 ⋊ C2 |
| Hall | C32×C5 ⋊ #120 |
| Sylow | C5 ⋊ C32×#120 |
780 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 222 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)(7,8,10,11,9)(13,15)(16,17,18,19);(4,5,6)(12,13)(14,15);(8,9)(10,11)(17,19)306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×#120, C3⋊D3×#4028, #72230246 |
| maximal normal subgroup of | C32×D5×#120, C3⋊D3×#4028, #72230246 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4125);