Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×C9⋊AGL(1,𝔽5) |
| Fitting | C5×Q8×C9 ⋊ C4 |
| Hall | C5×C9 ⋊ C4×Q8 |
| Sylow | C9 ⋊ Q8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ Q8×Dic9 |
210 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 210 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) = 360 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1565);