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 ⋊ #6891 |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
Polycyclic presentation:
3^5,7|a^3=d,b^a=bd,c^a=ce,f^b=f^4117 conjugacy classes — view the full character table.
| maximal subgroup of | #72249144, #72249184, #72254885 |
| maximal normal subgroup of | #72249144, #72249184, #72254885 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 181);