Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic961⋊C5 |
| unambiguous semidirect product | (C961⋊C5)⋊C4 |
| derived, Sylow | C961 ⋊ C4×C5 |
| Hall | C961⋊C5 ⋊ C4 |
| Hall | Dic961 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D961⋊C5 |
| commutator, hypocenter | C961 | C4×C5 |
| Frattini, socle | C2×C31 | D31⋊C5 |
| Fitting, cosocle | C2×C961 | C2×C5 |
| prime radical | C2×C961⋊C5 | C2 |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3844 |
Polycyclic presentation:
2,5,31,2,31|a^2=d,c^31=e^30,c^a=c^30e,e^a=e^30,c^b=c^16e^19,e^b=e^16212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 2);