Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | #10589650⋊C3 |
| Fitting | C4×D4×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ #532 |
977 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^4,3,2^2,3^2|b^2=g,h^3=i,c^a=cg,d^a=dg,h^a=h^2i^2,i^a=i^2,d^c=df,h^e=hi^2164 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/9)×#532, #72252828, #72268986, … |
| maximal normal subgroup of | AGL(1,ℤ/9)×#532, #72252828, #72268986, … |
| maximal quotient of | #72252828 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18715);