Finite Group DatabasebetaFinite Group Databasebeta| order | 21866 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D377 |
| unambiguous semidirect product | C13⋊(C29×D29) |
| unambiguous semidirect product | C29⋊(D13×C29) |
| Fitting, socle, Hall | C13×C292 ⋊ C2 |
| derived | C13×C29 ⋊ C2×C29 |
| Sylow | C292 ⋊ D13 |
| Sylow | C13 ⋊ C29×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D377 |
| commutator, cosocle, hypocenter | C13×C29 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C13×C292 | C2 |
| LCS | G ▷ C13×C29 | |
| UCS | C1 ◁ C29 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 754 |
5510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21866, 9);