Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×Q8×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×2−1+4 |
2538 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^3|c^2=f,d^2=f,g^3=i,e^a=ef,g^a=g^2i^2,i^a=i^2,e^b=ef,h^b=h^2,d^c=df159 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30823);