Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C292 · Schur multiplier (H2) = C29 |
| direct product | C292×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×C292) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×C292) |
| unambiguous semidirect product | (D7×C29)⋊(C3×C29) |
| Fitting, socle, Hall | C7×C292 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C2×C3×C292 |
| Hall | ΓL(1,𝔽8)×C292 ⋊ C2 |
| Hall | D7×C292 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×C292 |
| Hall | D7 ⋊ C3×C292 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C292 | AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7 | C2×C3×C292 |
| Frattini | C1 | G |
| Fitting, socle | C7×C292 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C292 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5887 |
5887 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 63);