Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
374 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 36 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:
2^2,3,2^3,3^2,2|a^2=i,d^2=i,e^2=i,f^2=i,b^a=bd,d^a=di,g^a=g^2,h^a=h^2,d^b=di,e^c=ef,f^c=e,g^c=gh,f^e=fi62 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13365);