Finite Group DatabasebetaFinite Group Databasebeta| order | 20586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊(D73⋊C3) |
| unambiguous semidirect product | (C73⋊C3)⋊D47 |
| unambiguous semidirect product | D3431⋊C3 |
| Fitting, socle, derived, Hall | C47×C73 ⋊ C2×C3 |
| Hall | C47×C73⋊C3 ⋊ C2 |
| Hall | D3431 ⋊ C3 |
| Hall | C73⋊C3 ⋊ D47 |
| Sylow | C73 ⋊ C3×D47 |
| Sylow | C47 ⋊ D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C47×C73 | C2×C3 |
| LCS | G ▷ C47×C73 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3431 |
Polycyclic presentation:
2,3,47,73|c^a=c^46,d^a=d^72,d^b=d^8639 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20586, 12);