Finite Group DatabasebetaFinite Group Databasebeta| order | 32157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C397⋊C3)⋊C27 |
| derived, Sylow | C397 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #16813210 |
| commutator, hypocenter | C397 | C3×C27 |
| Frattini | C3 | C3×#16813210 |
| Fitting | C9×C397 | C9 |
| socle | C3×C397 | C3×C9 |
| prime radical | C3×C397⋊C3 | C9 |
| cosocle | #16813208 | C32 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C9 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10719 |
Polycyclic presentation:
3^4,397|a^3=c,c^3=d,e^a=e^79,e^b=e^34,e^c=e^362477 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32157, 56);