Finite Group DatabasebetaFinite Group Databasebeta| order | 29406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×(C13⋊C3)⋊D13 |
| unambiguous semidirect product | (C13⋊C3)⋊(D13×C29) |
| Fitting, socle, Hall | C132×C29 ⋊ C2×C3 |
| derived, Sylow | C132 ⋊ C2×C3×C29 |
| Hall | C13×C29×C13⋊C3 ⋊ C2 |
| Hall | C29×C13⋊D13 ⋊ C3 |
| Hall | C13×C13⋊C3 ⋊ C2×C29 |
| Hall | C13⋊D13 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | (C13⋊C3)⋊D13 |
| commutator, cosocle, hypocenter | C132 | C2×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C132×C29 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C29 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1131 |
1450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29406, 19);