Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×C8×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ #577 |
836 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|d^2=e,e^2=f,h^3=i,d^a=de,e^a=ef,g^a=g^2,c^b=cf,d^b=de,e^b=ef,h^b=h^2i^2,i^b=i^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 15846);