Finite Group DatabasebetaFinite Group Databasebeta| order | 1701 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C7×#733 ⋊ C3 |
| Sylow | C7 ⋊ #6878 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
Polycyclic presentation:
3^5,7|b^3=d^2,c^3=e^2,b^a=bc,c^a=cd,d^a=de,f^a=f^2,f^b=f^469 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 133);