Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C22×C42 |
| unambiguous semidirect product | C9⋊#5464 |
| Fitting | C9×H(3,𝔽4) ⋊ C3 |
| Sylow | H(3,𝔽4) ⋊ 3−1+2 |
242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
3^3,2^6|b^3=c,b^a=bc,d^a=de,e^a=d,f^a=fg,g^a=f,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, 18311);