Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | Q8×D9⋊C9 |
| unambiguous semidirect product | D9⋊(Q8×C9) |
| Fitting | Q8×C9⋊C9 ⋊ C2 |
| Sylow | C9⋊C9 ⋊ C2×Q8 |
195 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1085);