Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C9×Q16 ⋊ C22 |
| Sylow | C3×C9 ⋊ #576 |
866 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|c^2=f,d^2=f,e^2=f,g^3=i,b^a=bf,c^a=cf,d^a=df,g^a=g^2i^2,i^a=i^2,c^b=cf,d^b=df,h^b=h^2,d^c=de,e^c=ef,e^d=ef120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 16062);