Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×Q8×Dic15 |
| Hall | C32×C5 ⋊ C4×Q8 |
| Sylow | C32 ⋊ Q8×Dic5 |
| Sylow | C5 ⋊ C3×Q8×Dic3 |
318 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4356);