Finite Group DatabasebetaFinite Group Databasebeta| order | 32220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C179⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C179⋊(C9×AGL(1,𝔽5)) |
| Fitting, Hall | C5×C9×C179 ⋊ C4 |
| derived, Hall | C5×C179 ⋊ C4×C9 |
| Hall | C9×C179 ⋊ AGL(1,𝔽5) |
| Sylow | C179 ⋊ C9×AGL(1,𝔽5) |
| Hall | C5×C9 ⋊ Dic179 |
| Sylow | C5 ⋊ C9×Dic179 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8055 |
3249 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32220, 11);