Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C33×D8 ⋊ C22 |
| Sylow | C33 ⋊ #509 |
652 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 116 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|d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^2,h^a=h^2,c^b=cf,i^b=i^2,d^c=de,e^c=ef111 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 26267);