Finite Group DatabasebetaFinite Group Databasebeta| order | 19806 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D3301⋊C3 |
| unambiguous semidirect product | (C3301⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C3301 ⋊ C2×C3 |
| Hall | C3301⋊C3 ⋊ C2 |
| Hall | D3301 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3301 | C2×C3 |
| LCS | G ▷ C3301 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3301 |
Polycyclic presentation:
2,3,3301|c^a=c^3300,c^b=c^1726556 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19806, 1);