Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2523 |
| unambiguous semidirect product | C3⋊(C7×D841) |
| Fitting, Hall | C3×C7×C841 ⋊ C2 |
| derived, Hall | C3×C841 ⋊ C2×C7 |
| Hall | C7×C841 ⋊ D3 |
| Sylow | C841 ⋊ D3×C7 |
| Hall | C3×C7 ⋊ D841 |
| Sylow | C3 ⋊ C7×D841 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2523 |
| commutator, cosocle, hypocenter | C3×C841 | C2×C7 |
| Frattini | C29 | C7×D87 |
| Fitting | C3×C7×C841 | C2 |
| socle | C3×C7×C29 | D29 |
| LCS | G ▷ C3×C841 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17661 |
8841 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 14);