Finite Group DatabasebetaFinite Group Databasebeta| order | 32220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×D3×D179 |
| unambiguous semidirect product | (D3×C179)⋊(C2×C3×C5) |
| unambiguous semidirect product | (C3×D179)⋊(C2×C3×C5) |
| unambiguous semidirect product | D537⋊(C2×C3×C5) |
| Fitting, socle, Hall | C32×C5×C179 ⋊ C22 |
| derived | C3×C179 ⋊ C22×C3×C5 |
| Hall | C32×C179 ⋊ C22×C5 |
| Hall | C5×C179 ⋊ C2×C3×D3 |
| Sylow | C179 ⋊ C2×C3×C5×D3 |
| Hall | C32×C5 ⋊ C2×D179 |
| Sylow | C32 ⋊ C2×C5×D179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D3×D179 |
| commutator, cosocle, hypocenter | C3×C179 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C179 | C22 |
| LCS | G ▷ C3×C179 | |
| UCS | C1 ◁ C3×C5 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5370 |
4095 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32220, 51);