Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D7×#87705 |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C3 |
| Hall | C7×#87705 ⋊ C2 |
| Hall | C7×D7×C19 ⋊ C3 |
| Hall | C7×D7 ⋊ C19⋊C3 |
| Sylow | C72 ⋊ C2×C19⋊C3 |
| Sylow | C19 ⋊ D7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
235 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#11716328, D7×#11716326, D7×#11716322, … |
| maximal normal subgroup of | D7×#11716328, D7×#11716326, D7×#11716322, … |
| maximal quotient of | Dic7×#87705, C2×D7×#87705, D7×#11924777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 75);