Finite Group DatabasebetaFinite Group Databasebeta| order | 1701 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C7 ⋊ C81⋊C3 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
Polycyclic presentation:
3^5,7|a^3=c,c^3=d,d^3=e,b^a=be,f^a=f^2261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 128);