Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22 |
| direct product | C2×D3×C9⋊A4 |
| unambiguous semidirect product | C3⋊(C22×C9⋊A4) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C9⋊A4) |
| unambiguous semidirect product | (C2×D3×C9)⋊A4 |
| Fitting | C23×C3×C9 ⋊ C2×C3 |
326 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3011);