Finite Group DatabasebetaFinite Group Databasebeta| order | 32220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C179⋊#157 |
| unambiguous semidirect product | C179⋊(C5×#157) |
| Fitting, socle, Hall | C32×C5×C179 ⋊ C4 |
| derived, Hall | C32×C179 ⋊ C4×C5 |
| Hall | C5×C179 ⋊ #157 |
| Sylow | C179 ⋊ C5×#157 |
| Hall | C32×C5 ⋊ Dic179 |
| Sylow | C32 ⋊ C5×Dic179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C179⋊#157 |
| commutator, hypocenter | C32×C179 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C179 | C4 |
| prime radical | C5×C3⋊D3×C179 | C2 |
| cosocle | C3⋊D3×C179 | C2×C5 |
| LCS | G ▷ C32×C179 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5370 |
2700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32220, 43);