Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C33 ⋊ #416 |
822 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^3|c^2=d,e^2=f,b^a=bf,c^a=cf,i^a=i^2,c^b=ce,e^b=ef,g^b=g^2,e^c=ef,h^c=h^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 21431);