Finite Group DatabasebetaFinite Group Databasebeta| order | 5766 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C312 · Schur multiplier (H2) = C31 |
| direct product | D3×C312 |
| unambiguous semidirect product | C3⋊(C2×C312) |
| Fitting, socle, Hall | C3×C312 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C312 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C312 | D3 |
| commutator, hypocenter | C3 | C2×C312 |
| Frattini | C1 | G |
| Fitting, socle | C3×C312 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C312 | |
136 conjugacy classes of subgroups.
2883 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C31×D31, D3×C31⋊D31, C2×D3×C312, … |
| maximal normal subgroup of | D3×C31×D31, D3×C31⋊D31, C2×D3×C312, … |
| maximal quotient of | Dic3×C312, C2×D3×C312, D9×C312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5766, 21);