Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D3×C8×C9 |
| Fitting | C32×C8×C9 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C8×C9 |
| Sylow | C32×C9 ⋊ C2×C8 |
280 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1512);