Finite Group DatabasebetaFinite Group Databasebeta| order | 7942 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C19 · Schur multiplier (H2) = C1 |
| direct product | C11×C19×D19 |
| unambiguous semidirect product | C19⋊(C2×C11×C19) |
| Fitting, socle, Hall | C11×C192 ⋊ C2 |
| derived | C19 ⋊ C2×C11×C19 |
| Sylow | C192 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C19 | D19 |
| commutator, hypocenter | C19 | C2×C11×C19 |
| Frattini | C1 | G |
| Fitting, socle | C11×C192 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C11×C19 | |
34 conjugacy classes of subgroups.
2299 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D192, C19×D11×D19, D19×D209, … |
| maximal normal subgroup of | C11×D192, C19×D11×D19, D19×D209, … |
| maximal quotient of | C11×C19×Dic19, C2×C11×C19×D19, C3×C11×C19×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7942, 6);