Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #88668⋊C3 |
| Fitting | C22×C3×3−1+2 ⋊ C22 |
| Sylow | C3×3−1+2 ⋊ C2×D4 |
438 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^3,3,2,3^3|f^3=h,c^a=ce,f^a=f^2h^2,h^a=h^2,c^b=ce,g^b=g^2,f^d=fh^281 conjugacy classes — view the full character table.
| maximal subgroup of | #72213202, C2×#88668⋊C3, #72219929, … |
| maximal normal subgroup of | C2×#88668⋊C3, #72219929, D3×D4×AGL(1,ℤ/9), … |
| maximal quotient of | #72213202, #72219901, #72219914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2346);