Finite Group DatabasebetaFinite Group Databasebeta| order | 9438 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C11×C13×D33 |
| unambiguous semidirect product | C3⋊(C11×C13×D11) |
| unambiguous semidirect product | C11⋊(D3×C11×C13) |
| Fitting, socle, Hall | C3×C112×C13 ⋊ C2 |
| derived | C3×C11 ⋊ C2×C11×C13 |
| Hall | C112×C13 ⋊ D3 |
| Hall | C3×C112 ⋊ C2×C13 |
| Sylow | C112 ⋊ D3×C13 |
| Hall | C3×C13 ⋊ C11×D11 |
| Sylow | C3 ⋊ C11×C13×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C13 | D33 |
| commutator, hypocenter | C3×C11 | C2×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C13 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C11×C13 | |
52 conjugacy classes of subgroups.
2574 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D13×D33, D3×C11×C13×D11, C11×D33⋊D13, … |
| maximal normal subgroup of | C11×D13×D33, D3×C11×C13×D11, C11×D33⋊D13, … |
| maximal quotient of | C11×C13×Dic33, C2×C11×C13×D33, C11×C13×D99, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9438, 37);