Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic36⋊C9 |
| Sylow | C9⋊C9 ⋊ Q16 |
97 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^2,3,2,3,2,3^2|a^2=f,b^2=df,c^3=e,d^2=f,g^3=h,b^a=bd,d^a=df,g^a=g^2h^2,h^a=h^2,g^c=gh^2159 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 253);