Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C33 ⋊ #456 |
858 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^3|b^2=e,c^2=def,d^2=f,e^2=f,b^a=be,c^a=cef,e^a=ef,i^a=i^2,c^b=cd,d^b=df,g^b=g^2,h^c=h^299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 22024);