Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D57 |
| unambiguous semidirect product | C3⋊(D19×C49) |
| unambiguous semidirect product | C19⋊(D3×C49) |
| Fitting, Hall | C3×C19×C49 ⋊ C2 |
| derived, Hall | C3×C19 ⋊ C2×C49 |
| Hall | C19×C49 ⋊ D3 |
| Hall | C3×C49 ⋊ D19 |
| Sylow | C19 ⋊ D3×C49 |
| Sylow | C3 ⋊ D19×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D57 |
| commutator, hypocenter | C3×C19 | C2×C49 |
| Frattini | C7 | C7×D57 |
| Fitting | C3×C19×C49 | C2 |
| socle | C3×C7×C19 | C2×C7 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
1470 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D19×C49, D49×D57, D57⋊D49, … |
| maximal normal subgroup of | D3×D19×C49, D49×D57, D57⋊D49, … |
| maximal quotient of | C49×Dic57, C2×C49×D57, C49×D171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 22);