Finite Group DatabasebetaFinite Group Databasebeta| order | 8322 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×D57 |
| unambiguous semidirect product | C3⋊(D19×C73) |
| unambiguous semidirect product | C19⋊(D3×C73) |
| Fitting, socle, Hall | C3×C19×C73 ⋊ C2 |
| derived, Hall | C3×C19 ⋊ C2×C73 |
| Hall | C19×C73 ⋊ D3 |
| Hall | C3×C73 ⋊ D19 |
| Sylow | C19 ⋊ D3×C73 |
| Sylow | C3 ⋊ D19×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | D57 |
| commutator, hypocenter | C3×C19 | C2×C73 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C73 | C2 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C73 | |
16 conjugacy classes of subgroups.
2190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D57×D73, D3×D19×C73, D57⋊D73, … |
| maximal normal subgroup of | D57×D73, D3×D19×C73, D57⋊D73, … |
| maximal quotient of | C73×Dic57, C2×C73×D57, C73×D171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8322, 11);