Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#91383 |
| Hall | C32×C5 ⋊ C22⋊Q8 |
| Sylow | C32 ⋊ #4092 |
| Sylow | C5 ⋊ C3×#897 |
322 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2789);