Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D11×#89204 |
| unambiguous semidirect product | C11⋊(C2×#89204) |
| derived, Hall | C72×C11 ⋊ C2×C9 |
| Hall | C11×#89204 ⋊ C2 |
| Hall | C72×D11 ⋊ C9 |
| Sylow | C72 ⋊ C9×D11 |
| Sylow | C11 ⋊ C2×#89204 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D11×#3861 |
| commutator, hypocenter | C72×C11 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C11 | C2×C3 |
| prime radical | C3×C72×D11 | C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
399 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#11725077, D11×#11725076, C2×D11×#89204 |
| maximal normal subgroup of | D11×#11725077, D11×#11725076, C2×D11×#89204 |
| maximal quotient of | Dic11×#89204, C2×D11×#89204 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 47);