Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C33 ⋊ C2×#104 |
1074 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^3|b^2=d,c^2=def,d^2=f,e^2=f,b^a=be,c^a=ce,e^a=ef,i^a=i^2,c^b=ce,e^b=ef,g^b=g^2,h^c=h^2114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10590393, #72220386, #72220388 |
| maximal normal subgroup of | D3×#10590393, #72220386, #72220388 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 21491);