Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#19097943 |
| Fitting, socle, Hall | C7×C292 ⋊ D3 |
| derived, Hall | C7×C292⋊C3 ⋊ C2 |
| Hall | C292⋊C3 ⋊ D7 |
| Sylow | C292 ⋊ D21 |
| Sylow | C7 ⋊ #19097943 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C292⋊C3 | C2 |
| Fitting, socle | C7×C292 | D3 |
| LCS | G ▷ C7×C292⋊C3 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 609 |
Polycyclic presentation:
2,3,7,29^2|b^a=b^2,c^a=c^6,d^a=de^5,e^a=e^28,d^b=d^8e,e^b=d^14e^201034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 70);