Finite Group DatabasebetaFinite Group Databasebeta| order | 29406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D169⋊C3 |
| unambiguous semidirect product | D169⋊(C3×C29) |
| unambiguous semidirect product | (C169⋊C3)⋊(C2×C29) |
| unambiguous semidirect product | (C29×D169)⋊C3 |
| Fitting, Hall | C29×C169 ⋊ C2×C3 |
| derived, Sylow | C169 ⋊ C2×C3×C29 |
| Hall | C29×C169⋊C3 ⋊ C2 |
| Hall | C29×D169 ⋊ C3 |
| Hall | C169⋊C3 ⋊ C2×C29 |
| Hall | D169 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C2×C3×C29 |
| Frattini | C13 | C29×D13⋊C3 |
| Fitting | C29×C169 | C2×C3 |
| socle | C13×C29 | D13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4901 |
986 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29406, 11);