Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | AGL(1,𝔽5)×C4⋊(C3⋊D3) |
| Fitting | C32×C4×C5 ⋊ C2×C4 |
| Hall | C32×C5 ⋊ C4×D4 |
| Sylow | C32 ⋊ D4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C4⋊(C3⋊D3) |
564 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 118 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.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4990);