Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C27⋊C16) |
| Sylow | C27 ⋊ C4⋊C16 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1728 |
Polycyclic presentation:
2^6,3^3|a^2=d,b^2=c,d^2=e,e^2=f,g^3=h,h^3=i,b^a=bc,g^a=g^2h^2i^2,h^a=h^2i^2,i^a=i^2456 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19);