Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | #10589595⋊C3 |
| Fitting | C2×C22⋊C4×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ #534 |
1104 conjugacy classes of subgroups; only the 252 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 252 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^4,3,2^2,3^2|d^2=f,h^3=i,c^a=cg,d^a=df,h^a=h^2i^2,i^a=i^2,d^b=dg,h^e=hi^2146 conjugacy classes — view the full character table.
| maximal subgroup of | #72268858, AGL(1,ℤ/9)×#534, #72268898 |
| maximal normal subgroup of | #72268858, AGL(1,ℤ/9)×#534, #72268898 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18446);