Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
292 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^3,3^3,2^3|b^2=i,c^2=i,g^2=i,h^2=i,b^a=bc,c^a=ci,e^a=e^2,f^a=f^2,c^b=ci,d^b=d^2,f^b=f^2,g^b=gh,h^b=hi,e^d=ef,g^d=h,h^d=ghi,h^g=hi44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 12447);