Finite Group DatabasebetaFinite Group Databasebeta| order | 32220 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊(C179⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C3⋊(C3×C179⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C179⋊(C3×ΓL(1,𝔽16)) |
| Fitting, socle, Hall | C32×C5×C179 ⋊ C4 |
| derived | C3×C5×C179 ⋊ C3×C4 |
| Hall | C32×C179 ⋊ AGL(1,𝔽5) |
| Hall | C5×C179 ⋊ C3×Dic3 |
| Sylow | C179 ⋊ C3×ΓL(1,𝔽16) |
| Hall | C32×C5 ⋊ Dic179 |
| Sylow | C32 ⋊ C179⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×Dic537 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5370 |
3231 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32220, 53);