Finite Group DatabasebetaFinite Group Databasebeta| order | 5766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C31 |
| unambiguous semidirect product | C3⋊(C31⋊D31) |
| unambiguous semidirect product | C31⋊D93 |
| Fitting, socle, derived, Hall | C3×C312 ⋊ C2 |
| Sylow | C312 ⋊ D3 |
| Sylow | C3 ⋊ C31⋊D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C312 | C2 |
| LCS | G ▷ C3×C312 | |
| UCS | C1 | |
136 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,31^2|b^a=b^2,c^a=c^30,d^a=d^301443 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C31⋊D31, D31×D93, C2×C3⋊(C31⋊D31), … |
| maximal normal subgroup of | D3×C31⋊D31, D31×D93, C2×C3⋊(C31⋊D31), … |
| maximal quotient of | C3⋊(C31⋊Dic31), C2×C3⋊(C31⋊D31), C9⋊(C31⋊D31), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5766, 23);