Finite Group DatabasebetaFinite Group Databasebeta| order | 9438 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C121 · Schur multiplier (H2) = C1 |
| direct product | D3×C13×C121 |
| unambiguous semidirect product | C3⋊(C2×C13×C121) |
| Fitting, Hall | C3×C13×C121 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C13×C121 |
| Hall | C3×C121 ⋊ C2×C13 |
| Hall | C3×C13 ⋊ C2×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C121 | D3 |
| commutator, hypocenter | C3 | C2×C13×C121 |
| Frattini | C11 | D3×C11×C13 |
| Fitting | C3×C13×C121 | C2 |
| socle | C3×C11×C13 | C2×C11 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C13×C121 | |
24 conjugacy classes of subgroups.
4719 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D13×C121, D3×C13×D121, D3×D1573, … |
| maximal normal subgroup of | D3×D13×C121, D3×C13×D121, D3×D1573, … |
| maximal quotient of | Dic3×C13×C121, C2×D3×C13×C121, C13×D9×C121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9438, 9);