Finite Group DatabasebetaFinite Group Databasebeta| order | 16660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C49⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C49⋊(C17×AGL(1,𝔽5)) |
| Fitting, Hall | C5×C17×C49 ⋊ C4 |
| derived, Hall | C5×C49 ⋊ C4×C17 |
| Hall | C17×C49 ⋊ AGL(1,𝔽5) |
| Hall | C5×C17 ⋊ Dic49 |
| Sylow | C49 ⋊ C17×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C17×Dic49 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4165 |
1717 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16660, 17);