Finite Group DatabasebetaFinite Group Databasebeta| order | 1701 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | #4428⋊C9 |
| Fitting | C7×C9⋊C9 ⋊ C3 |
| Sylow | C7 ⋊ C9×3−1+2 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
Polycyclic presentation:
3^5,7|a^3=e,b^3=d,c^3=e,b^a=bd,f^c=f^2165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 170);