Finite Group DatabasebetaFinite Group Databasebeta| order | 16986 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D447 |
| unambiguous semidirect product | C3⋊(C19×D149) |
| unambiguous semidirect product | C149⋊(D3×C19) |
| Fitting, socle, Hall | C3×C19×C149 ⋊ C2 |
| derived, Hall | C3×C149 ⋊ C2×C19 |
| Hall | C19×C149 ⋊ D3 |
| Sylow | C149 ⋊ D3×C19 |
| Hall | C3×C19 ⋊ D149 |
| Sylow | C3 ⋊ C19×D149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D447 |
| commutator, cosocle, hypocenter | C3×C149 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C149 | C2 |
| LCS | G ▷ C3×C149 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8493 |
4275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C19×D149, D19×D447, D57⋊D149, … |
| maximal normal subgroup of | D3×C19×D149, D19×D447, D57⋊D149, … |
| maximal quotient of | C19×Dic447, C2×C19×D447 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16986, 7);