Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #399 |
650 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^3|a^2=f,b^2=e,c^2=e,g^3=i,b^a=bf,c^a=cef,g^a=g^2i^2,i^a=i^2,c^b=cd,h^b=h^2186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 5656);