Finite Group DatabasebetaFinite Group Databasebeta| order | 17739 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊#14520299 |
| Sylow | C73 ⋊ C32⋊C27 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5913 |
Polycyclic presentation:
3^5,73|a^3=d,d^3=e,b^a=bc,f^a=f^2,f^d=f^8315 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17739, 317);