Finite Group DatabasebetaFinite Group Databasebeta| order | 19722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D173 |
| unambiguous semidirect product | C173⋊(D19⋊C3) |
| unambiguous semidirect product | D3287⋊C3 |
| Fitting, socle, derived, Hall | C19×C173 ⋊ C2×C3 |
| Hall | C19⋊C3×C173 ⋊ C2 |
| Hall | D3287 ⋊ C3 |
| Sylow | C173 ⋊ D19⋊C3 |
| Hall | C19⋊C3 ⋊ D173 |
| Sylow | C19 ⋊ C3×D173 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C173 | C2×C3 |
| LCS | G ▷ C19×C173 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3287 |
Polycyclic presentation:
2,3,19,173|c^a=c^18,d^a=d^172,c^b=c^7783 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19722, 12);