Finite Group DatabasebetaFinite Group Databasebeta| order | 17739 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C27×C73 ⋊ C9 |
| Sylow | C73 ⋊ #6875 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1971 |
Polycyclic presentation:
3^5,73|a^3=d,b^3=c,c^3=e,b^a=bc,c^a=ce,f^a=f^2,d^b=de^2,f^d=f^8251 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17739, 335);