Finite Group DatabasebetaFinite Group Databasebeta| order | 32157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊#16813210 |
| unambiguous semidirect product | (C3×#16813210)⋊C3 |
| Fitting | C32×C397 ⋊ C9 |
| Sylow | C397 ⋊ C32⋊C9 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3573 |
Polycyclic presentation:
3^4,397|a^3=d,b^a=bc,e^a=e^79,e^d=e^362429 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32157, 52);