Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×A4×C3⋊C8 |
| unambiguous semidirect product | C3⋊(C5×C8×A4) |
| unambiguous semidirect product | (C22×C3⋊C8)⋊(C3×C5) |
| unambiguous semidirect product | (C22×C5×C3⋊C8)⋊C3 |
| derived | C22×C3 ⋊ C3×C5×C8 |
116 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 360 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2547);