Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Sylow | C33 ⋊ #578 |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|b^2=f,d^2=ef,e^2=f,c^a=cf,g^a=g^2,h^a=h^2,d^b=de,e^b=ef,i^b=i^2,d^c=df126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 42770);