Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #568 |
938 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^3|a^2=e,b^2=e,e^2=f,g^3=i,d^a=df,g^a=g^2i^2,i^a=i^2,c^b=cf,h^b=h^2198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 16086);