Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D441 |
| unambiguous semidirect product | C9⋊(C11×D49) |
| unambiguous semidirect product | C49⋊(C11×D9) |
| Fitting, Hall | C9×C11×C49 ⋊ C2 |
| derived, Hall | C9×C49 ⋊ C2×C11 |
| Hall | C11×C49 ⋊ D9 |
| Hall | C9×C11 ⋊ D49 |
| Sylow | C49 ⋊ C11×D9 |
| Sylow | C9 ⋊ C11×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D441 |
| commutator, cosocle, hypocenter | C9×C49 | C2×C11 |
| Frattini | C3×C7 | C11×D21 |
| Fitting | C9×C11×C49 | C2 |
| socle | C3×C7×C11 | D21 |
| LCS | G ▷ C9×C49 | |
| UCS | C1 ◁ C11 | |
36 conjugacy classes of subgroups.
2442 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D441, C11×D9×D49, D99⋊D49, … |
| maximal normal subgroup of | D11×D441, C11×D9×D49, D99⋊D49, … |
| maximal quotient of | C11×Dic441, C2×C11×D441 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 11);