Finite Group DatabasebetaFinite Group Databasebeta| order | 32157 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C32×#16813210 |
| unambiguous semidirect product | (C397⋊C3)⋊(C3×C9) |
| Fitting, socle | C32×C397 ⋊ C9 |
| derived, Sylow | C397 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #16813210 |
| commutator, hypocenter | C397 | C32×C9 |
| Frattini | C1 | G |
| Fitting, socle | C32×C397 | C9 |
| prime radical | C32×C397⋊C3 | C3 |
| cosocle | C397⋊C3 | C33 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C32 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3573 |
477 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32157, 60);