Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×D19 |
| Fitting, socle, Hall | C3×C72×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C3×C72 |
| Hall | C72×C19 ⋊ C2×C3 |
| Hall | C3×C19 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | D19 |
| commutator, hypocenter | C19 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C72 | |
80 conjugacy classes of subgroups.
1617 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D7×D19, C3×D19×C7⋊D7, D3×C72×D19, … |
| maximal normal subgroup of | C3×C7×D7×D19, C3×D19×C7⋊D7, D3×C72×D19, … |
| maximal quotient of | C3×C72×Dic19, C2×C3×C72×D19, C72×C9×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 90);