Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C292 · Schur multiplier (H2) = C29 |
| direct product | D3×C7×C292 |
| unambiguous semidirect product | C3⋊(C2×C7×C292) |
| Fitting, socle, Hall | C3×C7×C292 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C7×C292 |
| Hall | C3×C292 ⋊ C2×C7 |
| Hall | C3×C7 ⋊ C2×C292 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C292 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C7×C292 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C292 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C7×C292 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17661 |
17661 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 80);