Finite Group DatabasebetaFinite Group Databasebeta| order | 29406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D507 |
| unambiguous semidirect product | C3⋊(C29×D169) |
| unambiguous semidirect product | C169⋊(D3×C29) |
| Fitting, Hall | C3×C29×C169 ⋊ C2 |
| derived, Hall | C3×C169 ⋊ C2×C29 |
| Hall | C29×C169 ⋊ D3 |
| Sylow | C169 ⋊ D3×C29 |
| Hall | C3×C29 ⋊ D169 |
| Sylow | C3 ⋊ C29×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D507 |
| commutator, cosocle, hypocenter | C3×C169 | C2×C29 |
| Frattini | C13 | C29×D39 |
| Fitting | C3×C29×C169 | C2 |
| socle | C3×C13×C29 | D13 |
| LCS | G ▷ C3×C169 | |
| UCS | C1 ◁ C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14703 |
7395 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29406, 8);