Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
206 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^2,3,2^3,3,2,3|a^2=d,b^2=dh,e^2=h,f^2=h,g^3=i,b^a=bdh,g^a=g^2i^2,i^a=i^2,e^c=ef,f^c=e,g^c=gi^2,f^e=fh83 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13166);