Finite Group DatabasebetaFinite Group Databasebeta| order | 17739 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×C9×C73 ⋊ C9 |
| Sylow | C73 ⋊ #6868 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1971 |
Polycyclic presentation:
3^5,73|a^3=d,b^3=e^2,b^a=bc,c^a=ce,f^a=f^2,f^d=f^8267 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17739, 321);