Finite Group DatabasebetaFinite Group Databasebeta| order | 32157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊#16813208 |
| Sylow | C397 ⋊ C32⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×C397⋊C3 |
| commutator | C3×C397 | C3×C9 |
| Fitting, prime radical | C33×C397 | C3 |
| socle, cosocle | C32×C397 | C32 |
| hypercenter | C33 | C397⋊C3 |
| hypocenter | C397 | C32⋊C9 |
| LCS | G ▷ C3×C397 ▷ C397 | |
| UCS | C1 ◁ C32 ◁ C33 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10719 |
Polycyclic presentation:
3^4,397|a^3=d,b^a=bc,e^a=e^3623597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32157, 19);