Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C841⋊C7 |
| unambiguous semidirect product | (C2×C841)⋊(C3×C7) |
| unambiguous semidirect product | (C2×C3×C841)⋊C7 |
| Fitting, Hall | C2×C3×C841 ⋊ C7 |
| derived, Sylow | C841 ⋊ C2×C3×C7 |
| Hall | C3×C841 ⋊ C2×C7 |
| Hall | C2×C841 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C841⋊C7 |
| commutator, cosocle, hypocenter | C841 | C2×C3×C7 |
| Frattini | C29 | C2×C3×C29⋊C7 |
| Fitting | C2×C3×C841 | C7 |
| socle | C2×C3×C29 | C29⋊C7 |
| LCS | G ▷ C841 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5046 |
762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 5);