Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#14584115 |
| Fitting, socle, Hall | C2×C72×C19 ⋊ C3 |
| derived, Hall | C72×C19 ⋊ C2×C3 |
| Hall | C2×C72 ⋊ C19⋊C3 |
| Sylow | C72 ⋊ C2×C19⋊C3 |
| Hall | C2×C19 ⋊ #3861 |
| Sylow | C19 ⋊ C2×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14584115 |
| commutator, hypocenter | C72×C19 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
626 conjugacy classes — view the full character table.
| maximal subgroup of | #26013817, #26013819, #26013827, … |
| maximal normal subgroup of | #26013817, #26013819, #26013827, … |
| maximal quotient of | C4×#14584115, C22×#14584115, C2×#22552709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 86);