Finite Group DatabasebetaFinite Group Databasebeta| order | 1701 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C7×C32⋊C9 ⋊ C3 |
| Sylow | C7 ⋊ C9⋊H(3,𝔽3) |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
Polycyclic presentation:
3^5,7|b^3=d,b^a=bd,c^a=ce,f^a=f^4,f^b=f^2117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 188);