Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | Dic6×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×Dic6) |
| unambiguous semidirect product | (C3×AGL(1,ℤ/9))⋊Q8 |
| unambiguous semidirect product | (D9×Dic6)⋊C3 |
| Sylow | C3×3−1+2 ⋊ C2×Q8 |
294 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2276);