Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | #10589621⋊C3 |
| Sylow | 3−1+2 ⋊ #544 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^4,3,2^2,3^2|a^2=g,c^2=g,d^2=f,h^3=i,c^a=cg,d^a=df,h^a=h^2i^2,i^a=i^2,c^b=cf,h^e=hi^2146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18596);