Finite Group DatabasebetaFinite Group Databasebeta| order | 32186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D847 |
| unambiguous semidirect product | C7⋊(C19×D121) |
| unambiguous semidirect product | C121⋊(D7×C19) |
| Fitting, Hall | C7×C19×C121 ⋊ C2 |
| derived, Hall | C7×C121 ⋊ C2×C19 |
| Hall | C19×C121 ⋊ D7 |
| Hall | C7×C19 ⋊ D121 |
| Sylow | C121 ⋊ D7×C19 |
| Sylow | C7 ⋊ C19×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D847 |
| commutator, cosocle, hypocenter | C7×C121 | C2×C19 |
| Frattini | C11 | C19×D77 |
| Fitting | C7×C19×C121 | C2 |
| socle | C7×C11×C19 | D11 |
| LCS | G ▷ C7×C121 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16093 |
8075 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32186, 7);