Finite Group DatabasebetaFinite Group Databasebeta| order | 5890 |
| automorphism | Aut(G) order 6361200 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2945 |
| unambiguous semidirect product | C5⋊D589 |
| unambiguous semidirect product | C19⋊D155 |
| unambiguous semidirect product | C31⋊D95 |
| Fitting, socle, derived, Hall | C5×C19×C31 ⋊ C2 |
| Hall | C19×C31 ⋊ D5 |
| Hall | C5×C31 ⋊ D19 |
| Hall | C5×C19 ⋊ D31 |
| Sylow | C31 ⋊ D95 |
| Sylow | C19 ⋊ D155 |
| Sylow | C5 ⋊ D589 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C19×C31 | C2 |
| LCS | G ▷ C5×C19×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,19,31|b^a=b^4,c^a=c^18,d^a=d^301474 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D95, D19×D155, D5×D589, … |
| maximal normal subgroup of | D31×D95, D19×D155, D5×D589, … |
| maximal quotient of | Dic2945, C2×D2945, C3×D2945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5890, 9);