Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×#168 |
| unambiguous semidirect product | (C22×#168)⋊C32 |
| unambiguous semidirect product | (C22×C3×#168)⋊C3 |
| derived | C22×C5 ⋊ C32×C8 |
| Hall | C22×#168 ⋊ C32 |
| Sylow | C5 ⋊ C3×C8×A4 |
136 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2540);