Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C3⋊(D29⋊C7) |
| unambiguous semidirect product | C3⋊(C29×D29⋊C7) |
| unambiguous semidirect product | D87⋊(C7×C29) |
| unambiguous semidirect product | (C29⋊C7)⋊(D3×C29) |
| Fitting, socle, Hall | C3×C292 ⋊ C2×C7 |
| derived | C3×C29 ⋊ C2×C7×C29 |
| Hall | C3×C29×C29⋊C7 ⋊ C2 |
| Hall | C29×C29⋊C7 ⋊ D3 |
| Hall | C29×D87 ⋊ C7 |
| Sylow | C292 ⋊ D3×C7 |
| Sylow | C3 ⋊ C29×D29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C3⋊(D29⋊C7) |
| commutator, cosocle, hypocenter | C3×C29 | C2×C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C292 | C2×C7 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C29 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1218 |
783 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 37);