Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #67×ΓL(1,𝔽16) |
| Fitting | C22×C32×C5 ⋊ C2×C4 |
| Hall | C32×C5 ⋊ C4×D4 |
| Sylow | C32 ⋊ D4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic3×#67 |
410 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×ΓL(1,𝔽16), D3×AGL(1,𝔽5)×#67, #72229996, … |
| maximal normal subgroup of | D3×D4×ΓL(1,𝔽16), D3×AGL(1,𝔽5)×#67, #72229996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5036);