Finite Group DatabasebetaFinite Group Databasebeta| order | 17748 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C17×C29 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic3×C17×C29 |
| unambiguous semidirect product | C3⋊(C3×C4×C17×C29) |
| derived | C3 ⋊ C3×C4×C17×C29 |
| Hall | C32×C17×C29 ⋊ C4 |
| Hall | C32×C29 ⋊ C4×C17 |
| Hall | C32×C17 ⋊ C4×C29 |
| Sylow | C32 ⋊ C4×C17×C29 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5916 |
8874 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17748, 41);