Finite Group DatabasebetaFinite Group Databasebeta| order | 32220 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C179 · Schur multiplier (H2) = C1 |
| direct product | C3×ΓL(1,𝔽16)×C179 |
| unambiguous semidirect product | C3⋊(C3×AGL(1,𝔽5)×C179) |
| Fitting, socle, Hall | C32×C5×C179 ⋊ C4 |
| derived | C3×C5 ⋊ C3×C4×C179 |
| Hall | C32×C179 ⋊ AGL(1,𝔽5) |
| Hall | C5×C179 ⋊ C3×Dic3 |
| Hall | C32×C5 ⋊ C4×C179 |
| Sylow | C32 ⋊ AGL(1,𝔽5)×C179 |
| Sylow | C5 ⋊ C3×Dic3×C179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C179 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C3×C4×C179 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C179 | C4 |
| prime radical | C32×D5×C179 | C2 |
| cosocle | C3×D5 | C2×C3×C179 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C3×C179 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5370 |
4833 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32220, 52);