Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | (C29⋊D29)⋊ΓL(1,𝔽8) |
| Fitting, socle, derived, Hall | C7×C292 ⋊ C2×C3 |
| Hall | C7⋊(C292⋊C3) ⋊ C2 |
| Hall | C7×C29⋊D29 ⋊ C3 |
| Hall | C29⋊D29 ⋊ ΓL(1,𝔽8) |
| Sylow | C292 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ (C29⋊D29)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C292 | C2×C3 |
| LCS | G ▷ C7×C292 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 609 |
Polycyclic presentation:
2,3,7,29^2|d^a=d^28,e^a=e^28,c^b=c^2,d^b=d^10e^20,e^b=d^22e^18990 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 66);