Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#14584107 |
| Fitting, Hall | C2×C19×C49 ⋊ C3 |
| derived, Hall | C19×C49 ⋊ C2×C3 |
| Hall | C2×C49 ⋊ C19⋊C3 |
| Sylow | C49 ⋊ C2×C19⋊C3 |
| Hall | C2×C19 ⋊ C49⋊C3 |
| Sylow | C19 ⋊ C2×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14584107 |
| commutator, hypocenter | C19×C49 | C2×C3 |
| Frattini | C7 | C2×#87704 |
| Fitting | C2×C19×C49 | C3 |
| socle | C2×C7×C19 | ΓL(1,𝔽8) |
| LCS | G ▷ C19×C49 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
626 conjugacy classes — view the full character table.
| maximal subgroup of | #26013744, #26013748, #26013750, … |
| maximal normal subgroup of | #26013744, #26013748, #26013750, … |
| maximal quotient of | C4×#14584107, C22×#14584107, C2×#22552692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 16);