Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×D32×Q8 |
| Fitting | C32×C5×Q8 ⋊ C22 |
| Hall | C32×C5 ⋊ C22×Q8 |
| Sylow | C32 ⋊ C22×C5×Q8 |
662 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 244 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5647);