Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26044456 |
| Fitting, socle, derived, Hall | C3×C292 ⋊ C2×C7 |
| Hall | C3×#19154634 ⋊ C2 |
| Hall | #19154634 ⋊ D3 |
| Hall | C29×D87 ⋊ C7 |
| Sylow | C292 ⋊ D3×C7 |
| Sylow | C3 ⋊ #26044456 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C292 | C2×C7 |
| LCS | G ▷ C3×C292 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 174 |
Polycyclic presentation:
2,7,3,29^2|c^a=c^2,d^a=d^28,d^b=d^16,e^b=e^16207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 42);