Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D12×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×D12) |
| unambiguous semidirect product | (D9×D12)⋊C3 |
| Fitting | C3×C4×3−1+2 ⋊ C22 |
| Sylow | C3×3−1+2 ⋊ C2×D4 |
402 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 402 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) = 72 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #72219892, D3×D4×AGL(1,ℤ/9), #72219953, … |
| maximal normal subgroup of | D3×D4×AGL(1,ℤ/9), #72219953, #72219954, … |
| maximal quotient of | #72219892, #72220025, AGL(1,ℤ/9)×#626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2287);