Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C3×C42 |
No aliases for this group.
| Fitting | C3×C9×#120 ⋊ C2 |
| Sylow | C3×C9 ⋊ H(3,𝔽4) |
1300 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1300 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^6,3^3|h^3=i,c^a=cf,d^a=def,g^a=g^2,h^a=h^2i^2,i^a=i^2,c^b=ce,d^b=df201 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20076);