Finite Group DatabasebetaFinite Group Databasebeta| order | 19890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C13×C17 · Schur multiplier (H2) = C1 |
| direct product | C9×D5×C13×C17 |
| unambiguous semidirect product | C5⋊(C2×C9×C13×C17) |
| Fitting, Hall | C5×C9×C13×C17 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C9×C13×C17 |
| Hall | C5×C13×C17 ⋊ C2×C9 |
| Hall | C5×C9×C17 ⋊ C2×C13 |
| Hall | C5×C9×C13 ⋊ C2×C17 |
| Hall | C5×C17 ⋊ C2×C9×C13 |
| Hall | C5×C13 ⋊ C2×C9×C17 |
| Hall | C5×C9 ⋊ C2×C13×C17 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9945 |
7956 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19890, 6);