Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×C8×D9 |
| Fitting | C2×C5×C8×C9 ⋊ C2 |
| derived, Sylow | C9 ⋊ C22×C5×C8 |
| Hall | C5×C9 ⋊ C22×C8 |
228 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 779);