Finite Group DatabasebetaFinite Group Databasebeta| order | 32226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C131 · Schur multiplier (H2) = C1 |
| direct product | C131×D123 |
| unambiguous semidirect product | C3⋊(D41×C131) |
| unambiguous semidirect product | C41⋊(D3×C131) |
| Fitting, socle, Hall | C3×C41×C131 ⋊ C2 |
| derived, Hall | C3×C41 ⋊ C2×C131 |
| Hall | C41×C131 ⋊ D3 |
| Hall | C3×C131 ⋊ D41 |
| Sylow | C41 ⋊ D3×C131 |
| Sylow | C3 ⋊ D41×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C131 | D123 |
| commutator, cosocle, hypocenter | C3×C41 | C2×C131 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C131 | C2 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C131 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16113 |
8253 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32226, 7);