Finite Group DatabasebetaFinite Group Databasebeta| order | 29406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D377 |
| unambiguous semidirect product | C29⋊(D13×C13⋊C3) |
| Fitting, socle, derived, Hall | C132×C29 ⋊ C2×C3 |
| Hall | C13×C29×C13⋊C3 ⋊ C2 |
| Hall | C13×D377 ⋊ C3 |
| Hall | C13×C13⋊C3 ⋊ D29 |
| Sylow | C132 ⋊ C3×D29 |
| Sylow | C29 ⋊ D13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C29 | C2×C3 |
| LCS | G ▷ C132×C29 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2262 |
1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29406, 22);