Finite Group DatabasebetaFinite Group Databasebeta| order | 17556 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C19×Dic11 |
| unambiguous semidirect product | C11⋊(C3×C4×C7×C19) |
| derived, Sylow | C11 ⋊ C3×C4×C7×C19 |
| Hall | C3×C7×C11×C19 ⋊ C4 |
| Hall | C7×C11×C19 ⋊ C3×C4 |
| Hall | C3×C11×C19 ⋊ C4×C7 |
| Hall | C3×C7×C11 ⋊ C4×C19 |
| Hall | C11×C19 ⋊ C3×C4×C7 |
| Hall | C7×C11 ⋊ C3×C4×C19 |
| Hall | C3×C11 ⋊ C4×C7×C19 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17556 |
5586 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17556, 7);