Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D841⋊C7) |
| unambiguous semidirect product | D2523⋊C7 |
| unambiguous semidirect product | (C841⋊C7)⋊D3 |
| Fitting, derived, Hall | C3×C841 ⋊ C2×C7 |
| Hall | C3×C841⋊C7 ⋊ C2 |
| Hall | C841⋊C7 ⋊ D3 |
| Hall | D2523 ⋊ C7 |
| Sylow | C841 ⋊ D3×C7 |
| Sylow | C3 ⋊ D841⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C841 | C2×C7 |
| Frattini | C29 | C3⋊(D29⋊C7) |
| socle | C3×C29 | D29⋊C7 |
| LCS | G ▷ C3×C841 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2523 |
Polycyclic presentation:
2,7,3,29^2|d^29=e^28,c^a=c^2,d^a=d^28e,e^a=e^28,d^b=d^23e^10,e^b=e^23201 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 4);