Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3×C4 |
No aliases for this group.
| Fitting | C3×C9×#117 ⋊ C2 |
| Sylow | C3×C9 ⋊ #410 |
790 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^6,3^3|b^2=f,c^2=d,h^3=i,c^a=ce,d^a=df,g^a=g^2,h^a=h^2i^2,i^a=i^2,e^c=ef282 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 10448);