Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | #10589900⋊C3 |
| Sylow | 3−1+2 ⋊ #518 |
1132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^4,3,2^2,3^2|a^2=g,h^3=i,d^a=df,h^a=h^2i^2,i^a=i^2,c^b=cf,h^e=hi^2182 conjugacy classes — view the full character table.
| maximal subgroup of | #72268904, AGL(1,ℤ/9)×#518, #72268918 |
| maximal normal subgroup of | #72268904, AGL(1,ℤ/9)×#518, #72268918 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19687);