Finite Group DatabasebetaFinite Group Databasebeta| order | 29406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C1 |
| direct product | C169×D87 |
| unambiguous semidirect product | C3⋊(D29×C169) |
| unambiguous semidirect product | C29⋊(D3×C169) |
| Fitting, Hall | C3×C29×C169 ⋊ C2 |
| derived, Hall | C3×C29 ⋊ C2×C169 |
| Hall | C29×C169 ⋊ D3 |
| Hall | C3×C169 ⋊ D29 |
| Sylow | C29 ⋊ D3×C169 |
| Sylow | C3 ⋊ D29×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | D87 |
| commutator, hypocenter | C3×C29 | C2×C169 |
| Frattini | C13 | C13×D87 |
| Fitting | C3×C29×C169 | C2 |
| socle, cosocle | C3×C13×C29 | C2×C13 |
| prime radical | C13×D87 | C13 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C169 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14703 |
7605 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29406, 7);