Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| isoclinism | isoclinic class of D49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D49⋊C3 |
| unambiguous semidirect product | D49⋊(C3×C19) |
| unambiguous semidirect product | (C49⋊C3)⋊(C2×C19) |
| Fitting, Hall | C19×C49 ⋊ C2×C3 |
| derived, Sylow | C49 ⋊ C2×C3×C19 |
| Hall | C19×C49⋊C3 ⋊ C2 |
| Hall | C19×D49 ⋊ C3 |
| Hall | C49⋊C3 ⋊ C2×C19 |
| Hall | D49 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D49⋊C3 |
| commutator, hypocenter | C49 | C2×C3×C19 |
| Frattini | C7 | C19×AGL(1,𝔽7) |
| Fitting | C19×C49 | C2×C3 |
| socle | C7×C19 | AGL(1,𝔽7) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
266 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D49⋊C3, C2×C19×D49⋊C3, C19⋊C3×D49⋊C3, … |
| maximal normal subgroup of | D19×D49⋊C3, C2×C19×D49⋊C3, C19⋊C3×D49⋊C3, … |
| maximal quotient of | C19×(C49⋊C3)⋊C4, C2×C19×D49⋊C3, C19×D49⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 8);