Finite Group DatabasebetaFinite Group Databasebeta| order | 32220 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×C179⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C179⋊(C32×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C32×C5×C179 ⋊ C4 |
| derived, Hall | C5×C179 ⋊ C32×C4 |
| Hall | C32×C179 ⋊ AGL(1,𝔽5) |
| Sylow | C179 ⋊ C32×AGL(1,𝔽5) |
| Hall | C32×C5 ⋊ Dic179 |
| Sylow | C5 ⋊ C32×Dic179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C179⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C179 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C179 | C4 |
| prime radical | C32×D5×C179 | C2 |
| cosocle | D5×C179 | C2×C32 |
| LCS | G ▷ C5×C179 | |
| UCS | C1 ◁ C32 | |
72 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, 49);