Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×C72) |
| unambiguous semidirect product | (C19⋊C3)⋊(C2×C72) |
| Fitting, socle, Hall | C72×C19 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C2×C3×C72 |
| Hall | C72×C19⋊C3 ⋊ C2 |
| Hall | C72×D19 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C2×C72 |
| Hall | D19 ⋊ C3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C72 | |
80 conjugacy classes of subgroups.
441 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D7×D19⋊C3, C7⋊D7×D19⋊C3, C2×C72×D19⋊C3, … |
| maximal normal subgroup of | C7×D7×D19⋊C3, C7⋊D7×D19⋊C3, C2×C72×D19⋊C3, … |
| maximal quotient of | C72×(C19⋊C3)⋊C4, C2×C72×D19⋊C3, C72×#4294⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 26);