Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | D4⋊(C3⋊(C9⋊C8)) |
| Sylow | C3×C9 ⋊ D4⋊C8 |
410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^6,3^3|a^2=d,c^2=e,d^2=f,h^3=i,b^a=bc,c^a=ce,g^a=g^2,h^a=h^2i^2,i^a=i^2,c^b=ce288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 1959);