Finite Group DatabasebetaFinite Group Databasebeta| order | 10222 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C269 · Schur multiplier (H2) = C1 |
| direct product | D19×C269 |
| unambiguous semidirect product | C19⋊(C2×C269) |
| Fitting, socle, Hall | C19×C269 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C269 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C269 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C269 |
| Frattini | C1 | G |
| Fitting, socle | C19×C269 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C269 | |
8 conjugacy classes of subgroups.
2959 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D269, C2×D19×C269, C3×D19×C269, … |
| maximal normal subgroup of | D19×D269, C2×D19×C269, C3×D19×C269, … |
| maximal quotient of | Dic19×C269, C2×D19×C269, C3×D19×C269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10222, 1);