Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26044451 |
| Fitting, socle, Hall | C3×C292 ⋊ D7 |
| derived, Hall | C3×#19154637 ⋊ C2 |
| Hall | #19154637 ⋊ D3 |
| Sylow | C292 ⋊ D21 |
| Sylow | C3 ⋊ #26044451 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#19154637 | C2 |
| Fitting, socle | C3×C292 | D7 |
| LCS | G ▷ C3×#19154637 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 174 |
Polycyclic presentation:
2,3,7,29^2|b^a=b^2,c^a=c^6,d^a=d^24e^22,e^a=d^20e^5,d^c=d^23e^7,e^c=e^24234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 35);