Finite Group DatabasebetaFinite Group Databasebeta| order | 8702 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C229 · Schur multiplier (H2) = C1 |
| direct product | D19×C229 |
| unambiguous semidirect product | C19⋊(C2×C229) |
| Fitting, socle, Hall | C19×C229 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C229 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C229 | D19 |
| commutator, hypocenter | C19 | C2×C229 |
| Frattini | C1 | G |
| Fitting, socle | C19×C229 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C229 | |
8 conjugacy classes of subgroups.
2519 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D229, C2×D19×C229, C3×D19×C229, … |
| maximal normal subgroup of | D19×D229, C2×D19×C229, C3×D19×C229, … |
| maximal quotient of | Dic19×C229, C2×D19×C229, C3×D19×C229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8702, 3);