Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C5×#64090 |
| Fitting | C32×C5×C22⋊C4 ⋊ C2 |
| Hall | C32×C5 ⋊ C4×D4 |
| Sylow | C32 ⋊ C4×C5×D4 |
564 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 174 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) = 720 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3,4,5)(6,7,8,9)(11,13)(17,18,19);(10,11)(12,13)(14,15,16);(11,13)(15,16)(18,19)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4382);