Finite Group DatabasebetaFinite Group Databasebeta| order | 10982 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C289 · Schur multiplier (H2) = C1 |
| direct product | D19×C289 |
| unambiguous semidirect product | C19⋊(C2×C289) |
| Fitting, Hall | C19×C289 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | D19 |
| commutator, hypocenter | C19 | C2×C289 |
| Frattini | C17 | C17×D19 |
| Fitting | C19×C289 | C2 |
| socle, cosocle | C17×C19 | C2×C17 |
| prime radical | C17×D19 | C17 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C289 | |
12 conjugacy classes of subgroups.
3179 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D289, C2×D19×C289, D19⋊C3×C289, … |
| maximal normal subgroup of | D19×D289, C2×D19×C289, D19⋊C3×C289, … |
| maximal quotient of | Dic19×C289, C2×D19×C289, C3×D19×C289, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10982, 3);