Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C33 ⋊ #520 |
1430 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 1430 conjugacy classes of subgroups — too many to draw. Only its 255 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^3|c^2=f,d^2=e,b^a=bf,d^a=df,g^a=g^2,h^a=h^2,d^b=df,g^b=g^2,i^b=i^2,d^c=df144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 44418);