Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C27×C22⋊Q8 ⋊ C2 |
| Sylow | C27 ⋊ #563 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^6,3^3|b^2=f,d^2=f,g^3=h,h^3=i,c^a=cf,d^a=def,g^a=g^2h^2i^2,h^a=h^2i^2,i^a=i^2,c^b=ce,d^b=df201 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2447);