Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C3×D19×C49 |
| Fitting, Hall | C3×C19×C49 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C3×C49 |
| Hall | C19×C49 ⋊ C2×C3 |
| Hall | C3×C19 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C49 | D19 |
| commutator, hypocenter | C19 | C2×C3×C49 |
| Frattini | C7 | C3×C7×D19 |
| Fitting | C3×C19×C49 | C2 |
| socle | C3×C7×C19 | C2×C7 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C49 | |
24 conjugacy classes of subgroups.
1617 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D19×D49, D3×D19×C49, D19×D147, … |
| maximal normal subgroup of | C3×D19×D49, D3×D19×C49, D19×D147, … |
| maximal quotient of | C3×C49×Dic19, C2×C3×D19×C49, C9×D19×C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 18);