Finite Group DatabasebetaFinite Group Databasebeta| order | 32186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2299 |
| unambiguous semidirect product | C19⋊(C7×D121) |
| unambiguous semidirect product | C121⋊(C7×D19) |
| Fitting, Hall | C7×C19×C121 ⋊ C2 |
| derived, Hall | C19×C121 ⋊ C2×C7 |
| Hall | C7×C121 ⋊ D19 |
| Hall | C7×C19 ⋊ D121 |
| Sylow | C121 ⋊ C7×D19 |
| Sylow | C19 ⋊ C7×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2299 |
| commutator, cosocle, hypocenter | C19×C121 | C2×C7 |
| Frattini | C11 | C7×D209 |
| Fitting | C7×C19×C121 | C2 |
| socle | C7×C11×C19 | D11 |
| LCS | G ▷ C19×C121 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16093 |
8057 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32186, 4);