Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#11716328 |
| Fitting, socle, Hall | C72×C19 ⋊ C2×C3 |
| derived | C7×C19 ⋊ C2×C3×C7 |
| Hall | C7×#87705 ⋊ C2 |
| Hall | C7×D133 ⋊ C3 |
| Sylow | C72 ⋊ D19⋊C3 |
| Sylow | C19 ⋊ C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11716328 |
| commutator, hypocenter | C7×C19 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C2×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C7 | |
34 conjugacy classes of subgroups.
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 29);