Finite Group DatabasebetaFinite Group Databasebeta| order | 32220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic895 |
| unambiguous semidirect product | C179⋊(C9×Dic5) |
| derived, Hall | C5×C179 ⋊ C4×C9 |
| Hall | C5×C9×C179 ⋊ C4 |
| Hall | C9×C179 ⋊ Dic5 |
| Sylow | C179 ⋊ C9×Dic5 |
| Hall | C5×C9 ⋊ Dic179 |
| Sylow | C5 ⋊ C9×Dic179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D895 |
| commutator, hypocenter | C5×C179 | C4×C9 |
| Frattini | C2×C3 | C3×D895 |
| Fitting | C2×C5×C9×C179 | C2 |
| socle, prime radical, cosocle | C2×C3×C5×C179 | C2×C3 |
| LCS | G ▷ C5×C179 | |
| UCS | C1 ◁ C2×C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32220 |
8082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32220, 4);