Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #3699⋊C9 |
| Fitting | D4×C9⋊C9 ⋊ C2 |
| Sylow | C9⋊C9 ⋊ #41 |
212 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 212 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 |
Polycyclic presentation:
2^3,3,2,3^3|b^2=e,d^3=f,g^3=h,c^a=ce,g^a=g^2h^2,h^a=h^2,c^b=ce,g^d=gh^2150 conjugacy classes — view the full character table.
| maximal subgroup of | #72219896, #72219942 |
| maximal normal subgroup of | #72219896, #72219942 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1060);