Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| isoclinism | isoclinic class of #64422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#64422 |
| Fitting, socle, Hall | C72×C19 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C3×C19 |
| Hall | C19×#3862 ⋊ C2 |
| Hall | C7×D7×C19 ⋊ C3 |
| Hall | #3862 ⋊ C2×C19 |
| Hall | C7×D7 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #64422 |
| commutator, hypocenter | C72 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C19 | |
34 conjugacy classes of subgroups.
323 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#64422⋊C2, #64422⋊D19, D19×#64422, … |
| maximal normal subgroup of | C19×#64422⋊C2, #64422⋊D19, D19×#64422, … |
| maximal quotient of | C19×#10596872, C2×C19×#64422, C19×#11725075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 54);