Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19097943⋊C7 |
| Fitting, socle, Sylow | C292 ⋊ D3×C7 |
| derived, Hall | C292⋊C3 ⋊ C2×C7 |
| Hall | (C292⋊C3)⋊C7 ⋊ C2 |
| Hall | #19154634 ⋊ D3 |
| Hall | #19097943 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C292⋊C3 | C2×C7 |
| Fitting, socle | C292 | D3×C7 |
| LCS | G ▷ C292⋊C3 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 87 |
Polycyclic presentation:
2,7,3,29^2|c^a=c^2,d^a=de^3,e^a=e^28,d^b=d^20,e^b=e^20,d^c=d^7e^23,e^c=d^24e^2147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 18);