Finite Group DatabasebetaFinite Group Databasebeta| order | 10406 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D121 |
| unambiguous semidirect product | C121⋊(C2×C43) |
| Fitting, Hall | C43×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D121 |
| commutator, cosocle, hypocenter | C121 | C2×C43 |
| Frattini | C11 | D11×C43 |
| Fitting | C43×C121 | C2 |
| socle | C11×C43 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C43 | |
12 conjugacy classes of subgroups.
2666 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D121, C2×C43×D121, C3×C43×D121, … |
| maximal normal subgroup of | D43×D121, C2×C43×D121, C3×C43×D121, … |
| maximal quotient of | C43×Dic121, C2×C43×D121, C3×C43×D121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10406, 2);