Finite Group DatabasebetaFinite Group Databasebeta| order | 10626 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D483 |
| unambiguous semidirect product | C3⋊(C11×D161) |
| unambiguous semidirect product | C7⋊(C11×D69) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D483 |
| commutator, cosocle, hypocenter | C3×C7×C23 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C23 | C2 |
| LCS | G ▷ C3×C7×C23 | |
| UCS | C1 ◁ C11 | |
32 conjugacy classes of subgroups.
2673 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D21×D23, D11×D483, D253⋊D21, … |
| maximal normal subgroup of | C11×D21×D23, D11×D483, D253⋊D21, … |
| maximal quotient of | C11×Dic483, C2×C11×D483, C11×D1449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10626, 17);