Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | 3−1+2 ⋊ #519 |
876 conjugacy classes of subgroups; only the 452 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 452 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:
2^4,3,2^2,3^2|a^2=g,b^2=f,c^2=f,h^3=i,d^a=df,h^a=h^2i^2,i^a=i^2,c^b=cf,h^e=hi^2182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19732);