Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#10623979 |
| unambiguous semidirect product | D5⋊#3724 |
| Hall | C32×C5 ⋊ C2×C4⋊C4 |
| Sylow | C32 ⋊ C2×C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×#3724 |
422 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5054);