Finite Group DatabasebetaFinite Group Databasebeta| order | 10406 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C43 · Schur multiplier (H2) = C1 |
| direct product | C11×D11×C43 |
| unambiguous semidirect product | C11⋊(C2×C11×C43) |
| Fitting, socle, Hall | C112×C43 ⋊ C2 |
| derived | C11 ⋊ C2×C11×C43 |
| Sylow | C112 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C43 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C11×C43 |
| Frattini | C1 | G |
| Fitting, socle | C112×C43 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C11×C43 | |
26 conjugacy classes of subgroups.
3311 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D43, D112×C43, D11×D473, … |
| maximal normal subgroup of | C11×D11×D43, D112×C43, D11×D473, … |
| maximal quotient of | C11×C43×Dic11, C2×C11×D11×C43, C3×C11×D11×C43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10406, 9);