Finite Group DatabasebetaFinite Group Databasebeta| order | 32157 |
| automorphism | ? |
| homology | Abelianization (H1) = C81 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C397 ⋊ C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | #16813210 |
| commutator, hypocenter | C397 | C81 |
| Fitting | C9×C397 | C9 |
| socle, prime radical | C3×C397 | C27 |
| cosocle | #24924302 | C3 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C9 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32157 |
Polycyclic presentation:
3^4,397|a^3=b,b^3=c,c^3=d,e^a=e^79,e^b=e^362477 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32157, 50);