Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #410 |
526 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^3|a^2=f,b^2=e,h^3=i,g^a=g^2,c^b=cd,d^b=df,h^b=h^2i^2,i^b=i^2,e^c=ef153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 6476);