Finite Group DatabasebetaFinite Group Databasebeta| order | 10722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1787 |
| unambiguous semidirect product | C1787⋊(C2×C3) |
| Fitting, socle, Hall | C3×C1787 ⋊ C2 |
| derived, Sylow | C1787 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1787 |
| commutator, cosocle, hypocenter | C1787 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C1787 | C2 |
| LCS | G ▷ C1787 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
2685 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1787, C2×C3×D1787, C9×D1787, … |
| maximal normal subgroup of | D3×D1787, C2×C3×D1787, C9×D1787, … |
| maximal quotient of | C3×Dic1787, C2×C3×D1787, C9×D1787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10722, 2);