Finite Group DatabasebetaFinite Group Databasebeta| order | 5766 |
| isoclinism | isoclinic class of D31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D31⋊C3 |
| unambiguous semidirect product | D31⋊(C3×C31) |
| unambiguous semidirect product | (C31⋊C3)⋊(C2×C31) |
| Fitting, socle, Sylow | C312 ⋊ C2×C3 |
| derived | C31 ⋊ C2×C3×C31 |
| Hall | C31×C31⋊C3 ⋊ C2 |
| Hall | C31×D31 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D31⋊C3 |
| commutator, hypocenter | C31 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C312 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C31 | |
21 conjugacy classes of subgroups.
341 conjugacy classes — view the full character table.
| maximal subgroup of | D31×D31⋊C3, C2×C31×D31⋊C3, C31⋊C3×D31⋊C3, … |
| maximal normal subgroup of | D31×D31⋊C3, C2×C31×D31⋊C3, C31⋊C3×D31⋊C3, … |
| maximal quotient of | C31×(C31⋊C3)⋊C4, C2×C31×D31⋊C3, C31×D31⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5766, 8);