Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Sylow | C33 ⋊ #394 |
2372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|a^2=f,b^2=ef,c^2=df,b^a=be,c^a=cf,g^a=g^2,h^a=h^2,c^b=cd,i^b=i^2186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 26604);