Finite Group DatabasebetaFinite Group Databasebeta| order | 32157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C9×C397 ⋊ C9 |
| Sylow | C397 ⋊ C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#16813210 |
| commutator, socle | C3×C397 | C3×C9 |
| Fitting | C9×C397 | C9 |
| prime radical, cosocle | C3×C397⋊C3 | C32 |
| hypercenter | C9 | #16813210 |
| hypocenter | C397 | C9⋊C9 |
| LCS | G ▷ C3×C397 ▷ C397 | |
| UCS | C1 ◁ C3 ◁ C9 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3573 |
Polycyclic presentation:
3^4,397|a^3=d,b^3=c,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, 53);