Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D19×#3861 |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C3 |
| Hall | C19×#3861 ⋊ C2 |
| Hall | C72×D19 ⋊ C3 |
| Sylow | C72 ⋊ C3×D19 |
| Sylow | C19 ⋊ C2×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
209 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#64424, D19×#64423, C2×D19×#3861, … |
| maximal normal subgroup of | D19×#64424, D19×#64423, C2×D19×#3861, … |
| maximal quotient of | Dic19×#3861, C2×D19×#3861, D19×#89204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 68);