Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D216⋊C3 |
| Fitting | C8×C27⋊C3 ⋊ C2 |
| Sylow | C27⋊C3 ⋊ D8 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^2,3,2^2,3^3|b^2=de,d^2=e,f^3=g,g^3=h,b^a=bd,d^a=de,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,f^c=fh141 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 272);