Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C7×C292 ⋊ C2×C3 |
| derived | C7×C29 ⋊ C2×C3×C29 |
| Hall | ΓL(1,𝔽8)×C292 ⋊ C2 |
| Hall | C29×D203 ⋊ C3 |
| Sylow | C292 ⋊ AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C29×D29 |
| Sylow | C7 ⋊ C3×C29×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | ΓL(1,𝔽8)⋊D29 |
| commutator, cosocle, hypocenter | C7×C29 | C2×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C292 | C2×C3 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C29 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 406 |
2233 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 64);