Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #541 |
652 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|a^2=f,b^2=e,c^2=f,d^2=e,h^3=i,c^a=cf,d^a=de,g^a=g^2,c^b=cf,d^b=def,h^b=h^2i^2,i^b=i^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13511);