Finite Group DatabasebetaFinite Group Databasebeta| order | 10626 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1771 |
| unambiguous semidirect product | C11⋊(C3×D161) |
| unambiguous semidirect product | C23⋊(C3×D77) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1771 |
| commutator, cosocle, hypocenter | C7×C11×C23 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C23 | C2 |
| LCS | G ▷ C7×C11×C23 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
2661 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D23×D77, C3×D11×D161, C3×D7×D253, … |
| maximal normal subgroup of | C3×D23×D77, C3×D11×D161, C3×D7×D253, … |
| maximal quotient of | C3×Dic1771, C2×C3×D1771, C9×D1771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10626, 11);