Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
200 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^4,3^3,2^2|a^2=d,c^2=d,e^3=f,f^3=g,b^a=bc,c^a=cd,e^a=e^2f^2g^2,f^a=f^2g^2,g^a=g^2,h^a=hi,c^b=cd,h^e=i,i^e=hi99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2215);