Finite Group DatabasebetaFinite Group Databasebeta| order | 32289 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×C229⋊C3 |
| unambiguous semidirect product | C229⋊(C3×C47) |
| unambiguous semidirect product | (C47×C229)⋊C3 |
| Fitting, socle, Hall | C47×C229 ⋊ C3 |
| derived, Sylow | C229 ⋊ C3×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | C229⋊C3 |
| commutator, cosocle, hypocenter | C229 | C3×C47 |
| Frattini | C1 | G |
| Fitting, socle | C47×C229 | C3 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C47 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10763 |
3713 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32289, 1);