Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #362 |
270 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^6,3^3|a^2=d,b^2=f,c^2=e,d^2=f,e^2=f,h^3=i,b^a=bc,c^a=ce,e^a=ef,g^a=g^2,h^a=h^2i^2,i^a=i^2,c^b=cef,d^b=df,e^b=ef198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2020);