Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C27⋊(C42⋊C3) |
| Fitting | C42×C27 ⋊ C3 |
| Sylow | C42 ⋊ C27⋊C3 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
3^4,2^4|b^3=c,c^3=d,e^2=g,f^2=gh,b^a=bd,e^a=ef,f^a=egh,g^a=h,h^a=gh168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 220);