Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C4×C5×D3×A4 |
| unambiguous semidirect product | (C22×C4×D3)⋊(C3×C5) |
| unambiguous semidirect product | (C22×C4×C5×D3)⋊C3 |
| Fitting | C22×C3×C4×C5 ⋊ C2×C3 |
| derived | C22×C3 ⋊ C2×C3×C4×C5 |
276 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5418);