Finite Group DatabasebetaFinite Group Databasebeta| order | 16986 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D149 |
| unambiguous semidirect product | C149⋊(C2×C19⋊C3) |
| unambiguous semidirect product | (C19×D149)⋊C3 |
| Fitting, socle, derived, Hall | C19×C149 ⋊ C2×C3 |
| Hall | C19⋊C3×C149 ⋊ C2 |
| Hall | C19×D149 ⋊ C3 |
| Sylow | C149 ⋊ C2×C19⋊C3 |
| Sylow | C19 ⋊ C3×D149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C149 | C2×C3 |
| LCS | G ▷ C19×C149 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2831 |
684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C19⋊C3)⋊#10597010, D19⋊C3×D149, C19⋊C3×#10597010, … |
| maximal normal subgroup of | (C19⋊C3)⋊#10597010, D19⋊C3×D149, C19⋊C3×#10597010, … |
| maximal quotient of | C19⋊C3×Dic149, C2×C19⋊C3×D149 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16986, 10);