Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D9⋊C9 |
| unambiguous semidirect product | D9⋊(C2×C4×C9) |
| unambiguous semidirect product | (C2×C4×D9)⋊C9 |
| Fitting | C2×C4×C9⋊C9 ⋊ C2 |
| derived | C9 ⋊ C22×C4×C9 |
| Sylow | C9⋊C9 ⋊ C22×C4 |
275 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×D9⋊C9, C42×D9⋊C9, C2×C4×AGL(1,ℤ/27) |
| maximal normal subgroup of | C2×D4×D9⋊C9, C42×D9⋊C9 |
| maximal quotient of | C42×D9⋊C9, C2×C4×AGL(1,ℤ/27) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1014);