Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C3×C9×#126 ⋊ C2 |
| Sylow | C3×C9 ⋊ #553 |
1190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^6,3^3|c^2=e,d^2=f,h^3=i,b^a=bf,c^a=cf,d^a=df,g^a=g^2,h^a=h^2i^2,i^a=i^2,c^b=cf,d^b=de,d^c=df207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20307);