Finite Group DatabasebetaFinite Group Databasebeta| order | 20859 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C409⋊C3)⋊C17 |
| unambiguous semidirect product | (C409⋊C17)⋊C3 |
| Fitting, socle, derived, Sylow | C409 ⋊ C3×C17 |
| Hall | C409⋊C17 ⋊ C3 |
| Hall | C409⋊C3 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C409 | C3×C17 |
| LCS | G ▷ C409 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 409 |
Polycyclic presentation:
3,17,409|c^a=c^355,c^b=c^559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20859, 1);