Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10624200 |
| Hall | C32×C5 ⋊ C2×#41 |
| Sylow | C32 ⋊ C2×#711 |
| Sylow | C5 ⋊ C2×#3795 |
694 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5672);