Finite Group DatabasebetaFinite Group Databasebeta| order | 32121 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×C43⋊C9 |
| unambiguous semidirect product | C43⋊(C9×C83) |
| unambiguous semidirect product | (C43×C83)⋊C9 |
| derived, Sylow | C43 ⋊ C9×C83 |
| Hall | C43×C83 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C83 | C43⋊C3 |
| commutator, hypocenter | C43 | C9×C83 |
| Frattini | C3 | C83×C43⋊C3 |
| Fitting, socle, prime radical | C3×C43×C83 | C3 |
| cosocle | C3×C43 | C3×C83 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C83 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32121 |
4233 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32121, 2);