Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×C9⋊AGL(1,𝔽5) |
| Fitting | C5×D4×C9 ⋊ C4 |
| Hall | C5×C9 ⋊ C4×D4 |
| Sylow | C9 ⋊ D4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ D4×Dic9 |
282 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D9×AGL(1,𝔽5), D4×3−1+2⋊AGL(1,𝔽5), #72247573, … |
| maximal normal subgroup of | D4×D9×AGL(1,𝔽5), D4×3−1+2⋊AGL(1,𝔽5) |
| maximal quotient of | #72247573 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1563);