Finite Group DatabasebetaFinite Group Databasebeta| order | 5766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C3)⋊D31 |
| Fitting, socle, derived, Sylow | C312 ⋊ C2×C3 |
| Hall | C31×C31⋊C3 ⋊ C2 |
| Hall | C31⋊D31 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C312 | C2×C3 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,31^2|c^a=c^30,d^a=d^30,c^b=c^5206 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5766, 13);