Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22 |
| direct product | C2×S4×3−1+2 |
| unambiguous semidirect product | A4⋊(C22×3−1+2) |
| unambiguous semidirect product | (C2×A4)⋊(C2×3−1+2) |
| unambiguous semidirect product | (C2×C9×S4)⋊C3 |
| Fitting | C23×3−1+2 ⋊ D3 |
308 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×#5935, C2×S4×AGL(1,ℤ/9), 3−1+2×#5934, … |
| maximal normal subgroup of | C2×S4×AGL(1,ℤ/9), C4×S4×3−1+2, S4×3−1+2⋊C4, … |
| maximal quotient of | D5×S4×3−1+2, C4×S4×3−1+2, C2×#14517984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2988);