Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×(C2×D3)⋊C8 |
| unambiguous semidirect product | (C2×D3)⋊(C3×C5×C8) |
| Fitting | C2×C32×C5×C8 ⋊ C2 |
| Hall | C32×C5 ⋊ C22⋊C8 |
| Sylow | C32 ⋊ C5×C22⋊C8 |
222 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1296);