Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C33×SD16 ⋊ C22 |
| Sylow | C33 ⋊ C2×AGL(1,ℤ/8) |
2060 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^3|d^2=f,e^2=f,d^a=df,g^a=g^2,h^a=h^2,d^b=df,i^b=i^2,d^c=de,e^c=ef,e^d=ef105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×AGL(1,ℤ/8) |
| maximal normal subgroup of | D3×C3⋊D3×AGL(1,ℤ/8) |
| maximal quotient of | #72245230, #72268985 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 42797);