Finite Group DatabasebetaFinite Group Databasebeta| order | 17739 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | 3−1+2⋊#10620321 |
| Sylow | C73 ⋊ 3−1+2⋊C9 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5913 |
Polycyclic presentation:
3^5,73|a^3=d,b^3=e,b^a=bc,c^a=ce,f^a=f^8,c^b=ce843 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17739, 107);