Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C33 ⋊ #466 |
1180 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 1180 conjugacy classes of subgroups — too many to draw. Only its 148 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=e,b^2=e,c^2=def,d^2=f,e^2=f,c^a=ce,g^a=g^2,h^a=h^2,c^b=cd,i^b=i^2,d^c=df,e^c=ef132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 25394);