Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×C42×C5×D3 |
| Fitting | C32×C42×C5 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C42×C5 |
| Hall | C32×C5 ⋊ C2×C42 |
| Sylow | C32 ⋊ C2×C42×C5 |
462 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 276 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4199);