Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#10587204 |
| Fitting | C32×D4×C11 ⋊ C2 |
| Hall | C32×C11 ⋊ D8 |
| Sylow | C11 ⋊ C3×#213 |
| Sylow | C32 ⋊ #4323 |
104 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 264 |
261 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 319);