Finite Group DatabasebetaFinite Group Databasebeta| order | 17748 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×C17×D29 |
| unambiguous semidirect product | C29⋊(C22×C9×C17) |
| unambiguous semidirect product | (C2×C29)⋊(C2×C9×C17) |
| Fitting | C2×C9×C17×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C22×C9×C17 |
| Hall | C9×C17×C29 ⋊ C22 |
| Hall | C17×C29 ⋊ C22×C9 |
| Hall | C9×C29 ⋊ C22×C17 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8874 |
4896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17748, 36);