Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3⋊D3×#168 |
| derived, Hall | C32×C5 ⋊ C22×C8 |
| Sylow | C32 ⋊ C22×#168 |
| Sylow | C5 ⋊ C2×C8×C3⋊D3 |
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3136);