Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#10623978 |
| unambiguous semidirect product | D5⋊#3722 |
| Hall | C32×C5 ⋊ C2×C22⋊C4 |
| Sylow | C32 ⋊ C2×C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×#3722 |
662 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 662 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) = 120 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#626, C2×#13088417, #72230047, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#626, C2×#13088417, #72230047, … |
| maximal quotient of | #72230089, #72230156, #72230447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5053);