Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | C9⋊(#564⋊C3) |
| Fitting | C9×#564 ⋊ C3 |
| Sylow | #564 ⋊ 3−1+2 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
3^3,2^6|b^3=c,d^2=h,e^2=hi,f^2=hi,g^2=i,b^a=bc,d^a=de,e^a=dhi,f^a=fg,g^a=fi,h^a=i,i^a=hi,f^d=fh,g^d=gi,f^e=fi,g^e=ghi65 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18315);