Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | #10589623⋊C3 |
| Fitting | 3−1+2×#117 ⋊ C2 |
| Sylow | 3−1+2 ⋊ #518 |
1052 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^4,3,2^2,3^2|c^2=g,d^2=f,h^3=i,c^a=cg,h^a=h^2i^2,i^a=i^2,d^b=dg,h^e=hi^2182 conjugacy classes — view the full character table.
| maximal subgroup of | #72244698, #72268891, AGL(1,ℤ/9)×#518 |
| maximal normal subgroup of | #72244698, #72268891, AGL(1,ℤ/9)×#518 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18598);