Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | D4×D9⋊C9 |
| unambiguous semidirect product | D9⋊(D4×C9) |
| unambiguous semidirect product | (D4×D9)⋊C9 |
| Fitting | D4×C9⋊C9 ⋊ C2 |
| Sylow | C9⋊C9 ⋊ C2×D4 |
275 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 275 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) = 72 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#92265, #72219942, D4×AGL(1,ℤ/27), … |
| maximal normal subgroup of | D4×#92265, #72219942, C2×D4×D9⋊C9 |
| maximal quotient of | #72220016, D4×AGL(1,ℤ/27), C2×D4×D9⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1059);