Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(C9⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | D5⋊(C4⋊Dic9) |
| Fitting | C2×C4×C5×C9 ⋊ C4 |
| Hall | C5×C9 ⋊ C2×C4⋊C4 |
| Sylow | C9 ⋊ C2×C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C4⋊Dic9 |
276 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1560);