Finite Group DatabasebetaFinite Group Databasebeta| order | 35406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D281⋊C7 |
| unambiguous semidirect product | D281⋊(C7×C9) |
| unambiguous semidirect product | (C281⋊C7)⋊(C2×C9) |
| unambiguous semidirect product | (C9×D281)⋊C7 |
| Fitting, Hall | C9×C281 ⋊ C2×C7 |
| derived, Sylow | C281 ⋊ C2×C7×C9 |
| Hall | C9×C281⋊C7 ⋊ C2 |
| Hall | C9×D281 ⋊ C7 |
| Hall | C281⋊C7 ⋊ C2×C9 |
| Hall | D281 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D281⋊C7 |
| commutator, hypocenter | C281 | C2×C7×C9 |
| Frattini | C3 | C3×D281⋊C7 |
| Fitting | C9×C281 | C2×C7 |
| socle, cosocle | C3×C281 | C2×C3×C7 |
| prime radical | C3×D281⋊C7 | C3 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2529 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35406, 11);