Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C27 ⋊ SD64 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^6,3^3|a^2=f,c^2=de,d^2=ef,e^2=f,g^3=h,h^3=i,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^2h^2i^2,h^a=h^2i^2,i^a=i^2,c^b=cd,d^b=de,e^b=ef162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 79);