Finite Group DatabasebetaFinite Group Databasebeta| order | 8322 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×C73) |
| unambiguous semidirect product | (C19⋊C3)⋊(C2×C73) |
| Fitting, socle, Hall | C19×C73 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C2×C3×C73 |
| Hall | C19⋊C3×C73 ⋊ C2 |
| Hall | D19×C73 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C2×C73 |
| Hall | D19 ⋊ C3×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C3×C73 |
| Frattini | C1 | G |
| Fitting, socle | C19×C73 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C73 | |
16 conjugacy classes of subgroups.
657 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D73, C2×C73×D19⋊C3, C73×AGL(1,𝔽19), … |
| maximal normal subgroup of | D19⋊C3×D73, C2×C73×D19⋊C3, C73×AGL(1,𝔽19), … |
| maximal quotient of | C73×(C19⋊C3)⋊C4, C2×C73×D19⋊C3, C73×#4294⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8322, 18);